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REVIEW 4 major objections 5 minor 234 references

Black Hole Gravitational Phenomena in Higher-Order Curvature-Scalar Gravity

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Pith's one-line read This paper argues that the deformation parameter ξ of a higher-order curvature-scalar gravity black hole is tightly constrained by shadow-size measurements: for M87* the bound is ξ/M² ≲ 0.091, with a similar but looser bound from Sgr A*.

desk verdict Competent but rushed phenomenology: the Sgr A* shadow bound is not a black-hole constraint, since part of its allowed ξ range has no horizon. read the letter →

arxiv 2509.11985 v3 pith:KXSHNAM4 submitted 2025-09-15 gr-qc hep-th

A. A. Araújo Filho , N. Heidari , Iarley P. Lobo This is my paper
classification gr-qchep-th MSC 83C5783D05 PACS 04.70.-s
keywords higher-ordercurvature-scalargravityblackholeshadowquasinormalmodesgravitationallensingdeformationparameterM87*SgrA*SolarSystemtests
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper studies a static, spherically symmetric black hole metric that extends Schwarzschild by a positive parameter ξ introduced by higher-order curvature-scalar gravity. It works out the horizon structure, quasinormal-mode spectra for scalar, vector, tensor, and spinor perturbations, photon sphere, shadow radius, and gravitational lensing in both weak and strong deflection. The central result is observational: the measured angular shadow diameters of M87* and Sgr A* restrict ξ/M² to be below about 0.091 and 0.963, respectively, and Solar System tests bound ξ directly in square meters. If correct, the theory is not just a formal extension; it makes quantified predictions that current and near-future black hole imaging can check.

What carries the argument

The metric (1), whose g_tt resembles Reissner-Nordström with ξ playing the role of Q² and whose g_rr is deformed by a term 2M ξ^{3/2}/r^4; the effective potentials from the Klein-Gordon, Maxwell, axial gravitational, and Dirac equations, solved with the WKB method and time-domain integration; the null-geodesic impact parameter b_c = √(D/A)|_{r_photon}; the Gauss-Bonnet theorem for the weak deflection angle; and the strong-deflection expansion about the photon sphere. The single parameter ξ carries all deviations from Schwarzschild and is the quantity constrained.

What would settle it

Compute the odd-parity perturbation equations directly from the HOCG field equations (or from the effective fluid's action) and check whether δT_10, δT_12, δT_13 really vanish. If they do not vanish, the tensor QNM frequencies in Section III.C are wrong. Also, a future measurement of the M87* angular shadow diameter with a precision better than ~0.5 μas would test the relation Ω_sh = 39.612 − 6.602(ξ/M²) − 1.28372(ξ/M²)² μas: if the diameter exceeded 40.3 μas while the mass/distance values used here hold, the bound ξ/M² ≲ 0.091 would be violated.

Watch

Extended reading notes

Core claim

The authors compute that the photon sphere sits at r_ph = (3M + √(9M² − 8ξ))/2 and the shadow radius is R = 3√3 M − √3 ξ/(2M) − 7ξ²/(24√3 M³). Using the angular-diameter formula Ω_sh = 6.191165×10^(−8) γ/(π D/Mpc) (b_c/M) μas, they obtain for M87*: Ω_sh = 39.612 − 6.602(ξ/M²) − 1.28372(ξ/M²)² μas, so the observed lower bound of 39.00 μas forces 0 ≤ ξ/M² ≲ 0.091; for Sgr A* the analogous expression gives ξ/M² ≲ 0.963. They also find that increasing ξ makes all quasinormal modes longer-lived and that the weak-field deflection angle grows with ξ while the strong-field deflection angle shrinks.

Load-bearing premise

The paper takes the metric (1) as a given solution of higher-order curvature-scalar gravity and assumes that in axial perturbations the supporting anisotropic fluid contributes nothing to the stress-energy tensor; if either fails, the quasinormal-mode and shadow predictions built on them are not valid.

Editorial extensions

If this is right

  • For M87*, the observed angular shadow diameter puts an upper limit ξ/M² ≲ 0.091; for Sgr A*, ξ/M² ≲ 0.963.
  • Quasinormal modes of all spins (0, 1, 2, 1/2) become less damped as ξ grows, so ringdown signals would ring longer than in Schwarzschild.
  • The photon sphere radius and shadow radius both decrease as ξ increases, yielding a smaller apparent silhouette than for a Schwarzschild black hole of the same mass.
  • Weak-field light deflection is enhanced relative to Schwarzschild, while strong-field deflection is diminished.
  • Solar System tests yield: Mercury perihelion precession −9.15×10^18 m² ≤ ξ ≤ 1.83×10^18 m²; light deflection −1.94×10^13 m² ≤ ξ ≤ 3.87×10^12 m²; Shapiro time delay |ξ| ≤ 2.04×10^14 m².

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The dimensionless M87* bound (ξ/M² ≲ 0.091) is much tighter than the Sgr A* bound; future high-precision shadow measurements of more massive or closer black holes could push this down significantly.
  • The formal analogy between ξ and Q² in g_tt means these shadow and QNM predictions double as a template for Reissner-Nordström-like black holes with a specific effective charge, offering cross-checks with charged-black-hole probes.
  • Because the tensor perturbation analysis assumes the anisotropic fluid does not source axial modes (δT10=δT12=δT13=0), the tensor QNM branch is the most fragile prediction; re-deriving axial perturbations from the explicit HOCG field equations would confirm or refute it.
  • The Solar System bounds, converted to dimensionless form for solar-mass objects, are orders of magnitude looser than the shadow bound, suggesting strong-field observations dominate the currently accessible parameter space.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper studies the static, spherically symmetric metric (1) proposed in [91] as a black hole solution of higher-order curvature-scalar gravity. The metric has g_tt = 1 - 2M/r + ξ/r² and g_rr = 1/(1 - 2M/r + 2M ξ^{3/2}/r⁴). The authors compute event and Cauchy horizons, scalar, vector, tensor and spinor quasinormal modes by WKB and time-domain integration, photon spheres and shadows, weak- and strong-field lensing, and use EHT measurements of M87* and Sgr A*, together with Mercury precession, light deflection, and Shapiro delay, to constrain ξ. The headline numerical results are the EHT constraints 0 ≤ ξ/M² ≲ 0.091 (M87*) and 0 ≤ ξ/M² ≲ 0.963 (Sgr A*), plus the Solar System bounds in Table XVII.

Significance. The paper assembles a broad set of standard tools in a recognizable way and, if the calculations were correct, would provide a useful phenomenological catalog for this metric. The shadow, QNM, and lensing formulas are explicit and, given the imported metric and the chosen standard methods, depend on a single free parameter ξ. However, the quantitative conclusions are not currently reliable: the Sgr A* bound is internally inconsistent with Eq. (76), the allowed interval includes spacetimes without an event horizon, and the weak-deflection formula contains a factor-π error. These issues are load-bearing for the central claims and require correction.

major comments (4)
  1. [VII.B, Eq. (76)] Eq. (76) is printed as Ωsh = 53.23368.87226 - (ξ/M²) - 1.72516(ξ/M²)², which is not a valid expression. If the intended formula is 53.2336 - 8.87226 x - 1.72516 x², then setting Ωsh = 41.7 μas gives x ≈ 1.08, not 0.963 as claimed in the text. The displayed equation therefore does not support the headline Sgr A* constraint; the coefficient and the crossing point must be re-derived and corrected.
  2. [II, Eq. (4); IV; VII.B] The metric has B(r)=1-2M/r+2Mξ^{3/2}/r⁴. For x=r/M, B=0 iff x⁴-2x³+2(ξ/M²)^{3/2}=0. The minimum of x⁴-2x³ is -27/16 at x=3/2, so real positive roots exist only for ξ/M² < (27/32)^{2/3} ≈ 0.893. For ξ/M²=0.963, B(3M/2)≈0.04>0, so the spacetime has no event horizon. The approximate r_h in Eq. (4) is a small-ξ expansion and misses the horizon disappearance. Thus the Sgr A* interval 0 ≤ ξ/M² ≲ 0.963 is not a black-hole constraint and must be capped near 0.893. Moreover, the time-domain evolutions in Section IV use ξ=0.9 for M=1, above this threshold, so those profiles are not black-hole waveforms.
  3. [VIII.B, Eq. (81)] The weak-deflection formula begins with 4πM/b. The standard Gauss-Bonnet result for Schwarzschild in geometric units is 4M/b, and the paper's own Solar System derivation in Eq. (136) uses 4M/b. No convention is stated that would introduce a factor π. Consequently, the ξ-dependent terms in Eq. (81) need to be re-derived; as written, the leading ξ correction is negative, which also contradicts the text's statement that increasing ξ enhances the weak-field deflection.
  4. [III.C, Eq. (35)] The tensor-perturbation analysis imports the background metric from Ref. [91] and models the source as an effective anisotropic fluid. The axial sector is then closed by setting δT10=δT12=δT13=0 in Eq. (35). This is a nontrivial assumption: for the actual higher-order curvature-scalar theory, the scalar field and curvature couplings could source axial perturbations, and no field equations or perturbation equations from [91] are given to verify the decoupling. Unless the axial-sector decoupling is established, the tensor QNM frequencies in Tables IX-XI and the corresponding time-domain results are not demonstrably those of the theory. The manuscript should state this limitation explicitly or supply the missing derivation.
minor comments (5)
  1. [Eq. (76)] The printed formula '53.23368.87226-' is garbled; a coefficient is missing even apart from the crossing-point inconsistency.
  2. [X] Section X appears to use Planck units (M_sun=9.138×10^37, a=3.583×10^45), but this is never stated. Table XVII reports bounds in m², so the conversion convention should be explicit.
  3. [Eqs. (13), (38), (118)] Several equations have mangled notation: Eq. (13) contains unresolved 'r6 s' factors, Eq. (38) mixes ξ and ξ² inconsistently, and Eq. (118) contains (z-1)^4 terms whose convergence is not discussed.
  4. [Table IX] The table header says ℓ=1 at M=1.0, but all rows list M=0.5; the mass labeling should be harmonized.
  5. [References] Reference [65?] in the Introduction and [195?] in Section VII are malformed citations; the bibliography needs cleanup.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: central predictions are derived from an externally sourced metric and constrained by independent observations; self-citations are methodological only.

full rationale

The derivation chain is open: Eq. (1) is taken from the independent external solution [91] (Nashed–Zafar–Bamba), and all subsequent quantities—horizons, QNM potentials, photon sphere, shadow radius, lensing angles, and Solar-System bounds—are computed from that metric using standard, reproducible methods. No parameter is fitted to the quantity later called a prediction: the EHT bounds in Sec. VII are obtained by evaluating the analytic Ω_sh(ξ) expression and comparing it with independent measurements (42±3 μas for M87*, 48.7±7 μas for Sgr A*), which is parameter estimation against external data, not a fit disguised as a test. The Solar-System constraints in Sec. X are similarly derived from geodesic equations and matched to independent Mercury-precession, light-deflection, and Cassini time-delay data; they are not inputs to the shadow or QNM computations. Multiple self-citations appear (e.g., [172], [210], [213], [217]), but only for standard methodology—WKB approximation, axial Regge–Wheeler potential, Gaussian-curvature lensing, spinor potentials—and are not load-bearing for uniqueness or for a pre-fit result. The note in the Conclusion announcing an imminent companion paper does not affect the derivation chain. The apparent inconsistency that the Sgr A* bound 0≤ξ/M²≲0.963 extends beyond the horizon-existence threshold (~0.893) is a correctness/internal-consistency concern, not a circularity, since the bound is derived from the same metric without re-importing the conclusion.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The paper's central claim rests on the validity of the imported metric (1) and on standard perturbation/lensing formalisms. No new physical entities are introduced; ξ is a parameter of the existing solution. The main burdens are the unverified background solution and the anisotropic fluid assumption in the axial perturbation analysis.

free parameters (1)
  • ξ = 0 ≤ ξ/M² ≲ 0.091 (M87*); 0 ≤ ξ/M² ≲ 0.963 (Sgr A*, numerically inconsistent); -9.15×10^18 m² ≤ ξ ≤ 1.83×10^18 m² (Mercur
    The deformation parameter of the HOCG metric (Eq. 1), introduced in Ref [91]. The paper constrains it with observations but does not derive it. The positivity requirement from Sec. II conflicts with the negative lower bounds in Table XVII.
assumptions (6)
  • domain assumption Metric (1) is a valid black hole solution of higher-order curvature-scalar gravity supported by an effective anisotropic fluid
    Adopted from Ref [91] without verification; used throughout, e.g., Eq. (1) and Sec. III.C.
  • domain assumption Perturbing fields (scalar, vector, tensor, spinor) evolve as test fields on the fixed background without backreaction
    Stated in Sec. III.A: 'the scalar field is regarded purely as a probe'.
  • domain assumption Axial (odd-parity) metric perturbations decouple from the anisotropic fluid matter sector
    Sec. III.C, Eq. (35): δT10=δT12=δT13=0. Needed for the tensor QNM potential in Eq. (37).
  • standard math The optical metric and Gauss-Bonnet theorem apply to the weak-field deflection integral with the stated integration domain
    Sec. VIII.B, Eq. (80): uses the optical metric area element and truncates the mass expansion.
  • standard math Tsukamoto's strong-deflection formalism for asymptotically flat, static, spherically symmetric spacetimes applies to this metric
    Sec. IX, based on Ref [218].
  • domain assumption The Solar System exterior is described by the same metric (1) with the same parameter ξ, and the perturbative expansion in ξ and M/L is valid
    Sec. X, Eq. (124).

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Cite this review

Pith. "Pith review of Black Hole Gravitational Phenomena in Higher-Order Curvature-Scalar Gravity." pith.science (2026). https://pith.science/paper/KXSHNAM4

@misc{pith2026250911985,
  author       = {Pith},
  title        = {Pith review of: Black Hole Gravitational Phenomena in Higher-Order Curvature-Scalar Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KXSHNAM4}},
  note         = {Machine review of arXiv:2509.11985}
}
abstract

This work aims to explore the gravitational consequences of a recently proposed black hole solution presented in the literature [Phys. Dark Univ. 50 (2025) 102061]. We initiate our analyzes by taking into account the horizon structure, focusing on both the event and Cauchy horizons. Subsequently, we examine the quasinormal modes by considering all types of perturbations -- scalar, vector, tensor, and spinorial. To strengthen these results, we also compute the time-domain for each perturbation. Next, we turn to the study of optical properties of the black hole. In particular, we investigate null geodesics, the photon sphere and its stability, as well as the corresponding black hole shadows. Following this, we analyze gravitational lensing phenomena in two regimes: the weak-field limit, utilizing the Gauss-Bonnet theorem, and the strong deflection limit, employing Tsukamoto's approach. In addition, we confront the lensing observables with Event Horizon Telescope (EHT) data for $Sgr A^{*}$ and $M87^{*}$. Finally, constraints on the parameter $\xi$ -- which is introduced by higher-order curvature-scalar gravity, thereby differing from the Schwarzschild solution -- are estimated using Solar System measurements such as the precession of Mercury's orbit, gravitational light bending, and time delay (or Shapiro effect).

Figures

Figures reproduced from arXiv: 2509.11985 by the authors.

Figure 1
Figure 1. FIG. 1. The dependence of the event horizon [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The behavior of the Cauchy horizon [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The behavior of the scalar potential [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (22 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The profile of the vector perturbation potential [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The tensor perturbation potential [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The spinor perturbation potential [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The dynamics of scalar perturbations are shown by evolving the waveform [PITH_FULL_IMAGE:figures/full_fig_p029_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The logarithmic evolution of the scalar field amplitude, ln [PITH_FULL_IMAGE:figures/full_fig_p030_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. This figure shows the late–time behavior of the scalar field on a double–logarithmic scale, [PITH_FULL_IMAGE:figures/full_fig_p031_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The temporal evolution of the vector perturbation [PITH_FULL_IMAGE:figures/full_fig_p032_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. The time evolution of ln [PITH_FULL_IMAGE:figures/full_fig_p033_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. The double–logarithmic representation of [PITH_FULL_IMAGE:figures/full_fig_p034_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. It is shown the temporal evolution of the tensor perturbation [PITH_FULL_IMAGE:figures/full_fig_p035_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. It is displayed the logarithmic time profile of the tensor perturbation, showing ln [PITH_FULL_IMAGE:figures/full_fig_p036_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. The asymptotic (late time) regime of tensor perturbations using a double–logarithmic rep [PITH_FULL_IMAGE:figures/full_fig_p037_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Temporal evolution of the tensor perturbation [PITH_FULL_IMAGE:figures/full_fig_p038_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Logarithmic representation of the tensor perturbation, with ln [PITH_FULL_IMAGE:figures/full_fig_p039_17.png]
Figure 18
Figure 18. Figure 18: FIG. 18. Late–time behavior of tensor perturbations shown in a double–logarithmic plot, with ln [PITH_FULL_IMAGE:figures/full_fig_p040_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19. The geodesic trajectories are obtained through numerical integration using [PITH_FULL_IMAGE:figures/full_fig_p041_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. The shadow radius [PITH_FULL_IMAGE:figures/full_fig_p042_20.png]
Figure 21
Figure 21. Figure 21: FIG. 21. Angular shadow diameter Ω [PITH_FULL_IMAGE:figures/full_fig_p042_21.png]
Figure 22
Figure 22. Figure 22: FIG. 22. Angular shadow diameter Ω [PITH_FULL_IMAGE:figures/full_fig_p043_22.png]
Figure 23
Figure 23. Figure 23: FIG. 23. Gaussian curvature [PITH_FULL_IMAGE:figures/full_fig_p045_23.png]
Figure 24
Figure 24. Figure 24: illustrates how the deflection angle ˜α(b, ξ) varies with the black hole parameters. For a fixed impact parameter b = 0.5, increasing ξ systematically enhances the deflection, indicating that the higher–order corrections strengthen the gravitational lensing effect. IX…
Figure 25
Figure 25. Figure 25: FIG. 25. Deflection angle [PITH_FULL_IMAGE:figures/full_fig_p053_25.png]

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Reference graph

Works this paper leans on

234 extracted references · 4 linked inside Pith

  1. [91]

    G. G. L. Nashed, Usman Zafar, and Kazuharu Bamba. An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field.Physics of the Dark Universe, 50:102061, 2025

    2025

  2. [1]

    Gravitational collapse and spacetime singularities.Physical Review Letters, 14(3):57, 1965

    Roger Penrose. Gravitational collapse and spacetime singularities.Physical Review Letters, 14(3):57, 1965

    1965

  3. [2]

    Cambridge university press, 2023

    Stephen W Hawking and George FR Ellis.The large scale structure of space-time. Cambridge university press, 2023

    2023

  4. [3]

    Cambridge University Press, 2007

    Pankaj S Joshi.Gravitational collapse and spacetime singularities. Cambridge University Press, 2007

    2007

  5. [4]

    Gw170817: observation of gravitational waves from a binary neutron star inspiral.Physical review letters, 119(16):161101, 2017

    Benjamin P Abbott, Rich Abbott, Thomas D Abbott, Fausto Acernese, Kendall Ackley, Carl Adams, Thomas Adams, Paolo Addesso, Rana X Adhikari, Vaishali B Adya, et al. Gw170817: observation of gravitational waves from a binary neutron star inspiral.Physical review letters, 119(16):161101, 2017

    2017

  6. [5]

    First M87 ∗ event horizon telescope results

    The Event Horizon Telescope Collaboration. First M87 ∗ event horizon telescope results. i. the shadow of the supermassive black hole.The Astrophysical Journal Letters, 875(1):L1, 2019

    2019

  7. [6]

    First sagittarius a∗ event horizon telescope results

    Kazunori Akiyama, Antxon Alberdi, Walter Alef, Juan Carlos Algaba, Richard Anantua, Keiichi Asada, Rebecca Azulay, Uwe Bach, Anne-Kathrin Baczko, David Ball, et al. First sagittarius a∗ event horizon telescope results. i. the shadow of the supermassive black hole in the center of the milky way.The Astrophysical Journal Letters, 930(2):L12, 2022. 63

    2022

  8. [7]

    Antonio De Felice and Shinji Tsujikawa.f(R) theories.Living Reviews in Relativity, 13(1):1–161, 2010

    2010

Show all 234 references
  1. [8]

    Thomas P Sotiriou and Valerio Faraoni.f(R) theories of gravity.Reviews of Modern Physics, 82(1):451–497, 2010

    2010

  2. [9]

    Introduction to modified gravity and gravitational alternative for dark energy.International Journal of Geometric Methods in Modern Physics, 4(01):115–145, 2007

    Shin’Ichi Nojiri and Sergei D Odintsov. Introduction to modified gravity and gravitational alternative for dark energy.International Journal of Geometric Methods in Modern Physics, 4(01):115–145, 2007

    2007

  3. [10]

    f(T) teleparallel gravity and cosmology.Reports on Progress in Physics, 79(10):106901, 2016

    Yi-Fu Cai, Salvatore Capozziello, Mariafelicia De Laurentis, and Emmanuel N Saridakis. f(T) teleparallel gravity and cosmology.Reports on Progress in Physics, 79(10):106901, 2016

    2016

  4. [11]

    Odintsov, and Vasilis K

    Shin’ichi Nojiri, Sergei D. Odintsov, and Vasilis K. Oikonomou. Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution.Physics Reports, 692:1–104, 2017

    2017

  5. [12]

    Odintsov, and Vasilis K

    Shin’ichi Nojiri, Sergei D. Odintsov, and Vasilis K. Oikonomou. k-essencef(R) gravity inflation. Nuclear Physics B, 941:11–27, 2019

    2019

  6. [13]

    Schwarzschild solution in extended teleparallel gravity.Europhysics Letters, 105(1):10001, 2014

    Gamal GL Nashed. Schwarzschild solution in extended teleparallel gravity.Europhysics Letters, 105(1):10001, 2014

    2014

  7. [14]

    Springer, 2011

    Valerio Faraoni and Salvatore Capozziello.Beyond Einstein gravity: a survey of gravitational theories for cosmology and astrophysics. Springer, 2011

    2011

  8. [15]

    Extended theories of gravity.Physics Reports, 509(4-5):167–321, 2011

    Salvatore Capozziello and Mariafelicia De Laurentis. Extended theories of gravity.Physics Reports, 509(4-5):167–321, 2011

    2011

  9. [16]

    Reconstruction of f(T)-gravity in the absence of matter

    W El Hanafy and Gamal GL Nashed. Reconstruction of f(T)-gravity in the absence of matter. Astrophysics and Space Science, 361(6):197, 2016

    2016

  10. [17]

    Vacuum non–singular black hole solutions in tetrad theory of gravitation

    Gamal GL Nashed. Vacuum non–singular black hole solutions in tetrad theory of gravitation. General Relativity and Gravitation, 34(7):1047–1058, 2002

    2002

  11. [18]

    Phase portraits of general f (t) cosmology.Journal of Cosmology and Astroparticle Physics, 2018(02):052, 2018

    Adel Awad, W El Hanafy, GGL Nashed, and Emmanuel N Saridakis. Phase portraits of general f (t) cosmology.Journal of Cosmology and Astroparticle Physics, 2018(02):052, 2018

    2018

  12. [19]

    Constant-roll infla- tion in f(T) teleparallel gravity.Journal of Cosmology and Astroparticle Physics, 2018(07):026, 2018

    Adel Awad, W El Hanafy, GGL Nashed, SD Odintsov, and VK Oikonomou. Constant-roll infla- tion in f(T) teleparallel gravity.Journal of Cosmology and Astroparticle Physics, 2018(07):026, 2018

    2018

  13. [20]

    Kerr-nut black hole thermodynamics in f(T) gravity theories.The European Physical Journal Plus, 130(7):124, 2015

    Gamal GL Nashed. Kerr-nut black hole thermodynamics in f(T) gravity theories.The European Physical Journal Plus, 130(7):124, 2015

    2015

  14. [21]

    Analytic models of anisotropic strange stars in f (t) gravity with off-diagonal tetrad.Astrophysics and Space Science, 361(1):27, 2016

    M Zubair and G Abbas. Analytic models of anisotropic strange stars in f (t) gravity with off-diagonal tetrad.Astrophysics and Space Science, 361(1):27, 2016

    2016

  15. [22]

    Possible formation of compact stars in f(R,T) gravity

    M Zubair, G Abbas, and I Noureen. Possible formation of compact stars in f(R,T) gravity. Astrophysics and Space Science, 361(1), 2015. 64

    2015

  16. [23]

    f (r, t) gravity

    Tiberiu Harko, Francisco SN Lobo, Shin’ichi Nojiri, and Sergei D Odintsov. f (r, t) gravity. Physical Review D, 84(2):024020, 2011

    2011

  17. [24]

    Interior solutions of compact stars in f (t, t) gravity under karmarkar condition.Physics of the Dark Universe, 30:100592, 2020

    Rabia Saleem, Faisal Kramat, and M Zubair. Interior solutions of compact stars in f (t, t) gravity under karmarkar condition.Physics of the Dark Universe, 30:100592, 2020

    2020

  18. [25]

    Dark energy in modified gauss-bonnet gravity: Late-time acceleration and¡? format?¿ the hierarchy problem.Physical Review D, 73(8):084007, 2006

    Guido Cognola, Emilio Elizalde, Shin’ichi Nojiri, Sergei D Odintsov, and Sergio Zerbini. Dark energy in modified gauss-bonnet gravity: Late-time acceleration and¡? format?¿ the hierarchy problem.Physical Review D, 73(8):084007, 2006

    2006

  19. [26]

    Charged black hole solutions in f(R,T) gravity coupled to nonlinear electrodynamics

    Gabriel I R´ ois, Jos´ e Tarciso SS Junior, Francisco SN Lobo, Manuel E Rodrigues, and Tiberiu Harko. Charged black hole solutions in f(R,T) gravity coupled to nonlinear electrodynamics. Physical Review D, 111(12):124044, 2025

    2025

  20. [27]

    A Ara´ ujo Filho, N Heidari, I

    A. A Ara´ ujo Filho, N Heidari, I. P Lobo, and VB Bezerra. Gravitational signatures of a nonlinear electrodynamics in f (r, t) gravity.Journal of Cosmology and Astroparticle Physics, 2025(09):015, 2025

    2025

  21. [28]

    Constrainingf(R) gravity by the large-scale structure.Universe, 1(2):123–157, 2015

    Ivan De Martino, Mariafelicia De Laurentis, and Salvatore Capozziello. Constrainingf(R) gravity by the large-scale structure.Universe, 1(2):123–157, 2015

    2015

  22. [29]

    Spectrum of relict gravitational radiation and the early state of the universe

    AA Starobinskii. Spectrum of relict gravitational radiation and the early state of the universe. JETP Letters, 30(11):682–685, 1979

    1979

  23. [30]

    Neutron and quark stars inf(R) gravity

    Artyom V Astashenok. Neutron and quark stars inf(R) gravity. InInternational Journal of Modern Physics: Conference Series, volume 41, page 1660130. World Scientific, 2016

    2016

  24. [31]

    Astashenok, Salvatore Capozziello, and Sergei D

    Artyom V. Astashenok, Salvatore Capozziello, and Sergei D. Odintsov. Maximal neutron star mass and the resolution of the hyperon puzzle in modified gravity.Physical Review D, 89(10):103509, 2014

    2014

  25. [33]

    The realistic models of relativistic stars inf(R) =R+αR 2 gravity.Classical and Quantum Gravity, 34(20):205008, 2017

    Artyom V Astashenok, Sergei D Odintsov, and Alvaro De la Cruz-Dombriz. The realistic models of relativistic stars inf(R) =R+αR 2 gravity.Classical and Quantum Gravity, 34(20):205008, 2017

    2017

  26. [34]

    Astashenok, Salvatore Capozziello, and Sergei D

    Artyom V. Astashenok, Salvatore Capozziello, and Sergei D. Odintsov. Nonperturbative models of quark stars inf(R) gravity.Physics Letters B, 742:160–166, 2015

    2015

  27. [35]

    Thermodynam- ical correspondence off(R) gravity in the jordan and einstein frames.International Journal of Modern Physics D, 29(13):2050090, 2020

    Gamal GL Nashed, W El Hanafy, Sergei D Odintsov, and Vasilis K Oikonomou. Thermodynam- ical correspondence off(R) gravity in the jordan and einstein frames.International Journal of Modern Physics D, 29(13):2050090, 2020

    2020

  28. [36]

    Anisotropic compact stars inf(R) gravity.The 65 European Physical Journal C, 81(5):481, 2021

    Gamal GL Nashed and Salvatore Capozziello. Anisotropic compact stars inf(R) gravity.The 65 European Physical Journal C, 81(5):481, 2021

    2021

  29. [37]

    Conformal transformations and weak field limit of scalar-tensor gravity.Physical Review D, 88(12):124011, 2013

    An Stabile and S Capozziello. Conformal transformations and weak field limit of scalar-tensor gravity.Physical Review D, 88(12):124011, 2013

    2013

  30. [38]

    Cosmological perfect- fluids inf(R) gravity.International Journal of Geometric Methods in Modern Physics, 16(01):1950008, 2019

    Salvatore Capozziello, Carlo Alberto Mantica, and Luca Guido Molinari. Cosmological perfect- fluids inf(R) gravity.International Journal of Geometric Methods in Modern Physics, 16(01):1950008, 2019

    2019

  31. [39]

    Effects of spatial curvature on thef(R) gravity phase space: no inflationary attractor?Classical and Quantum Gravity, 36(6):065008, 2019

    SD Odintsov and VK Oikonomou. Effects of spatial curvature on thef(R) gravity phase space: no inflationary attractor?Classical and Quantum Gravity, 36(6):065008, 2019

    2019

  32. [40]

    Physical Review D, 99(6):064049, 2019

    SD Odintsov and VK Oikonomou.f(R) gravity inflation with string-corrected axion dark matter. Physical Review D, 99(6):064049, 2019

    2019

  33. [41]

    Parth Shah and Gauranga C. Samanta. Stability analysis for cosmological models inf(R) gravity using dynamical system analysis.The European Physical Journal C, 79(5):414, 2019

    2019

  34. [42]

    Piattella, and J´ ulio C

    Tays Miranda, Celia Escamilla-Rivera, Oliver F. Piattella, and J´ ulio C. Fabris. Generic slow- roll and non-gaussianity parameters inf(R) theories.Journal of Cosmology and Astroparticle Physics,, 05:028, 2019

    2019

  35. [43]

    J. R. Nascimento, Gonzalo J. Olmo, P. J. Porfirio, A. Yu. Petrov, and A. R. Soares. Global Monopole in Palatinif(R) gravity.Physical Review D, 99(6):064053, 2019

    2019

  36. [44]

    Odintsov, Tanmoy Paul, and Diego S´ aez-Chill´ on G´ omez

    Emilio Elizalde, Sergei D. Odintsov, Tanmoy Paul, and Diego S´ aez-Chill´ on G´ omez. Inflation- ary universe inF(R) gravity with antisymmetric tensor fields and their suppression during its evolution.Physical Review D, 99(6):063506, 2019

    2019

  37. [45]

    Elizalde, S

    E. Elizalde, S. D. Odintsov, V. K. Oikonomou, and Tanmoy Paul. Logarithmic-correctedR 2 Gravity Inflation in the Presence of Kalb-Ramond Fields.Journal of Cosmology and Astropar- ticle Physics,, 02:017, 2019

    2019

  38. [46]

    Dynamical analysis of loop quantumR 2 cosmology.Physical Review D, 99(6):064025, 2019

    Long Chen. Dynamical analysis of loop quantumR 2 cosmology.Physical Review D, 99(6):064025, 2019

    2019

  39. [47]

    Piattella, and Sergio E

    Fulvio Sbis` a, Oliver F. Piattella, and Sergio E. Jor´ as. Pressure effects in the weak-field limit of f(R) =R+αR 2 gravity.Physical Review D, 99(10):104046, 2019

    2019

  40. [48]

    Samanta and Nisha Godani

    Gauranga C. Samanta and Nisha Godani. Validation of energy conditions in wormhole geometry within viablef(R) gravity.The European Physical Journal C, 79(7):623, 2019

    2019

  41. [49]

    Big bounce cosmology for PalatiniR 2 gravity with a Nieh–Yan term.The European Physical Journal C, 79(5):405, 2019

    Flavio Bombacigno and Giovanni Montani. Big bounce cosmology for PalatiniR 2 gravity with a Nieh–Yan term.The European Physical Journal C, 79(5):405, 2019

    2019

  42. [50]

    Grav- itational collapse in general relativity and in r 2-gravity: A comparative study.International Journal of Geometric Methods in Modern Physics, 16(03):1950035, 2019

    Artyom V Astashenok, Karim Mosani, Sergey D Odintsov, and Gauranga C Samanta. Grav- itational collapse in general relativity and in r 2-gravity: A comparative study.International Journal of Geometric Methods in Modern Physics, 16(03):1950035, 2019. 66

    2019

  43. [51]

    Charged solution with equal metric ansatz in gauss–bonnet theory coupled to scalar field.Physics of the Dark Universe, 41:101260, 2023

    GGL Nashed. Charged solution with equal metric ansatz in gauss–bonnet theory coupled to scalar field.Physics of the Dark Universe, 41:101260, 2023

    2023

  44. [52]

    Nojiri, S

    S. Nojiri, S. D. Odintsov, V. K. Oikonomou, and Arkady A. Popov. Ghost-freeF(R,G) gravity. Nuclear Physics B, 973:115617, 2021

    2021

  45. [53]

    Finite-time cosmological singularities and the possible fate of the universe.Physics Reports, 1034:1–114, 2023

    Jaume de Haro, Shin’ichi Nojiri, Sergei D Odintsov, Vasilis K Oikonomou, and Supriya Pan. Finite-time cosmological singularities and the possible fate of the universe.Physics Reports, 1034:1–114, 2023

    2023

  46. [54]

    Salvatore Capozziello and G. G. L. Nashed. Charged spherically symmetric black holes in scalar- tensor gauss–bonnet gravity.Classical and Quantum Gravity, 40(20):205023, 2023

    2023

  47. [55]

    Global dynamics in einstein- gauss-bonnet scalar field cosmology with matter.Physical Review D, 108(2):023519, 2023

    Alfredo D Millano, Genly Leon, and Andronikos Paliathanasis. Global dynamics in einstein- gauss-bonnet scalar field cosmology with matter.Physical Review D, 108(2):023519, 2023

    2023

  48. [56]

    F (q) f(q) gravity with gauss–bonnet corrections: From early-time inflation to late-time acceleration.Fortschritte der Physik, 72(9-10):2400113, 2024

    Shin’ichi Nojiri and Sergei D Odintsov. F (q) f(q) gravity with gauss–bonnet corrections: From early-time inflation to late-time acceleration.Fortschritte der Physik, 72(9-10):2400113, 2024

    2024

  49. [57]

    Traversable wormholes with static spherical symmetry and their stability in higher-curvature gravity.Journal of Cosmology and Astroparticle Physics, 2023(10):038, 2023

    M Ilyas and Kazuharu Bamba. Traversable wormholes with static spherical symmetry and their stability in higher-curvature gravity.Journal of Cosmology and Astroparticle Physics, 2023(10):038, 2023

    2023

  50. [58]

    Gauss–Bonnet AdS planar and spherical black hole thermodynamics and holography.Classical Quantum and Gravity, 41(23):235010, 2024

    Souvik Paul, Sunandan Gangopadhyay, and Ashis Saha. Gauss–Bonnet AdS planar and spherical black hole thermodynamics and holography.Classical Quantum and Gravity, 41(23):235010, 2024

    2024

  51. [59]

    G. G. L. Nashed. Spherically symmetric charged black holes inf(R) gravitational theories.The European Physical Journal Plus, 133(1):18, 2018

    2018

  52. [60]

    G. G. L. Nashed. Higher dimensional charged black hole solutions inf(R) gravitational theories. Advances in High Energy Physics, 2018:7323574, 2018

    2018

  53. [61]

    Spherically symmetric solutions of modified field equations inf(R) theories of gravity.Physical Review D, 74(6):064022, 2006

    T Multam¨ aki and Iiro Vilja. Spherically symmetric solutions of modified field equations inf(R) theories of gravity.Physical Review D, 74(6):064022, 2006

    2006

  54. [62]

    Rotating charged black hole spacetimes in quadraticf(R) gravitational theories

    GGL Nashed. Rotating charged black hole spacetimes in quadraticf(R) gravitational theories. International Journal of Modern Physics D, 27(07):1850074, 2018

    2018

  55. [63]

    Noether symmetries and analytical solutions in f(T) cosmology: A complete study.Physical Review D, 88(10):103526, 2013

    S Basilakos, Salvatore Capozziello, M De Laurentis, A Paliathanasis, and M Tsamparlis. Noether symmetries and analytical solutions in f(T) cosmology: A complete study.Physical Review D, 88(10):103526, 2013

    2013

  56. [64]

    Extended theories of gravity and their cosmo- logical and astrophysical applications.General Relativity and Gravitation, 40(2):357–420, 2008

    Salvatore Capozziello and Mauro Francaviglia. Extended theories of gravity and their cosmo- logical and astrophysical applications.General Relativity and Gravitation, 40(2):357–420, 2008

    2008

  57. [65]

    Charged spherically symmetric black holes in f(R) gravity and their stability analysis.Physical Review D, 99(10):104018, 2019

    Gamal GL Nashed and Salvatore Capozziello. Charged spherically symmetric black holes in f(R) gravity and their stability analysis.Physical Review D, 99(10):104018, 2019. 67

    2019

  58. [66]

    de la Cruz-Dombriz, A

    A. de la Cruz-Dombriz, A. Dobado, and A. L. Maroto. Black holes inf(R) theories.Physical Review D, 80(12):124011, 2009

    2009

  59. [67]

    A no-hair theorem for spherically symmetric black holes inR 2 gravity.General Relativity and Gravitation, 50(11):137, 2018

    Joseph Sultana and Demosthenes Kazanas. A no-hair theorem for spherically symmetric black holes inR 2 gravity.General Relativity and Gravitation, 50(11):137, 2018

    2018

  60. [68]

    A no-hair theorem for black holes inf(R) gravity.Classical and Quantum Gravity, 35(2):025018, 2017

    Pedro Ca˜ nate. A no-hair theorem for black holes inf(R) gravity.Classical and Quantum Gravity, 35(2):025018, 2017

    2017

  61. [69]

    On static and spherically symmetric solutions of starobinsky model.Research in Astronomy and Astrophysics, 18(12):157, 2018

    Shuang Yu, Chang-Jun Gao, and Ming-Jun Liu. On static and spherically symmetric solutions of starobinsky model.Research in Astronomy and Astrophysics, 18(12):157, 2018

    2018

  62. [70]

    Black hole solutions inR 2 gravity.Journal of High Energy Physics, 2015(5):1–20, 2015

    Alex Kehagias, Costas Kounnas, Dieter L¨ ust, and Antonio Riotto. Black hole solutions inR 2 gravity.Journal of High Energy Physics, 2015(5):1–20, 2015

    2015

  63. [71]

    Static solutions for fourth order gravity.Physical Review D, 82(10):104026, 2010

    William Nelson. Static solutions for fourth order gravity.Physical Review D, 82(10):104026, 2010

    2010

  64. [72]

    Spherically symmetric black holes inf(R) gravity: is geometric scalar hair supported?Classical and Quantum Gravity, 33(15):155005, 2016

    Pedro Ca˜ nate, Luisa G Jaime, and Marcelo Salgado. Spherically symmetric black holes inf(R) gravity: is geometric scalar hair supported?Classical and Quantum Gravity, 33(15):155005, 2016

    2016

  65. [73]

    On neutron stars inf(R) theories: Small radii, large masses and large energy emitted in a merger.Physics of the dark universe, 13:147–161, 2016

    Miguel Aparicio Resco, ´Alvaro de la Cruz-Dombriz, Felipe J Llanes Estrada, and V ´ ıctor Zapatero Castrillo. On neutron stars inf(R) theories: Small radii, large masses and large energy emitted in a merger.Physics of the dark universe, 13:147–161, 2016

    2016

  66. [74]

    Static and slowly rotating neutron stars in scalar–tensor theory with self-interacting massive scalar field

    Kalin V Staykov, Dimitar Popchev, Daniela D Doneva, and Stoytcho S Yazadjiev. Static and slowly rotating neutron stars in scalar–tensor theory with self-interacting massive scalar field. The European Physical Journal C, 78(7):586, 2018

    2018

  67. [75]

    Rapidly rotating neutron stars with a massive scalar field—structure and universal relations.Journal of Cosmology and Astroparticle Physics, 2016(11):019, 2016

    Daniela D Doneva and Stoytcho S Yazadjiev. Rapidly rotating neutron stars with a massive scalar field—structure and universal relations.Journal of Cosmology and Astroparticle Physics, 2016(11):019, 2016

    2016

  68. [76]

    Constraints on perturbativef(R) gravity via neutron stars.Journal of Cosmology and Astroparticle Physics, 2011(07):020, 2011

    Sava¸ s Arapo˘ glu, Cemsinan Deliduman, and K Yavuz Ek¸ si. Constraints on perturbativef(R) gravity via neutron stars.Journal of Cosmology and Astroparticle Physics, 2011(07):020, 2011

    2011

  69. [77]

    Equation-of-state of neutron stars with junction conditions in the starobinsky model.International Journal of Modern Physics D, 27(01):1750186, 2018

    Wei-Xiang Feng, Chao-Qiang Geng, Win-Fun Kao, and Ling-Wei Luo. Equation-of-state of neutron stars with junction conditions in the starobinsky model.International Journal of Modern Physics D, 27(01):1750186, 2018

    2018

  70. [78]

    Neutron stars in the starobinsky model.Physical Review D, 89(6):064019, 2014

    Apratim Ganguly, Radouane Gannouji, Rituparno Goswami, and Subharthi Ray. Neutron stars in the starobinsky model.Physical Review D, 89(6):064019, 2014

    2014

  71. [79]

    Slowly rotating neutron stars in scalar-tensor theories with a massive scalar field.Physical Review D, 93(8):084038, 2016

    Stoytcho S Yazadjiev, Daniela D Doneva, and Dimitar Popchev. Slowly rotating neutron stars in scalar-tensor theories with a massive scalar field.Physical Review D, 93(8):084038, 2016

    2016

  72. [80]

    Rapidly rotating neutron 68 stars in r-squared gravity.Physical Review D, 91(8):084018, 2015

    Stoytcho S Yazadjiev, Daniela D Doneva, and Kostas D Kokkotas. Rapidly rotating neutron 68 stars in r-squared gravity.Physical Review D, 91(8):084018, 2015

    2015

  73. [81]

    Non- perturbative and self-consistent models of neutron stars in r-squared gravity.Journal of Cos- mology and Astroparticle Physics, 2014(06):003, 2014

    Stoytcho S Yazadjiev, Daniela D Doneva, Kostas D Kokkotas, and Kalin V Staykov. Non- perturbative and self-consistent models of neutron stars in r-squared gravity.Journal of Cos- mology and Astroparticle Physics, 2014(06):003, 2014

    2014

  74. [82]

    Further stable neutron star models fromf(R) gravity.Journal of Cosmology and Astroparticle Physics, 2013(12):040, 2013

    Artyom V Astashenok, Salvatore Capozziello, and Sergei D Odintsov. Further stable neutron star models fromf(R) gravity.Journal of Cosmology and Astroparticle Physics, 2013(12):040, 2013

    2013

  75. [83]

    Struc- ture of neutron stars in-squared gravity.General Relativity and Gravitation, 45(4):771–783, 2013

    Mariana Orellana, Federico Garc ´ ıa, Florencia A Teppa Pannia, and Gustavo E Romero. Struc- ture of neutron stars in-squared gravity.General Relativity and Gravitation, 45(4):771–783, 2013

    2013

  76. [84]

    Mass- radius relation for neutron stars inf(R) gravity.Physical Review D, 93(2):023501, 2016

    Salvatore Capozziello, Mariafelicia De Laurentis, Ruben Farinelli, and Sergei D Odintsov. Mass- radius relation for neutron stars inf(R) gravity.Physical Review D, 93(2):023501, 2016

    2016

  77. [85]

    Neutron stars inf(R) gravity with per- turbative constraints.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 82(6):064033, 2010

    Alan Cooney, Simon DeDeo, and Dimitrios Psaltis. Neutron stars inf(R) gravity with per- turbative constraints.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 82(6):064033, 2010

    2010

  78. [86]

    Intermediate-range gravity: a generally covariant model.Physical Review Letters, 29(2):137, 1972

    John O’Hanlon. Intermediate-range gravity: a generally covariant model.Physical Review Letters, 29(2):137, 1972

    1972

  79. [87]

    1/Rgravity and scalar-tensor gravity.Physics Letters B, 575(1):1–3, 2003

    Takeshi Chiba. 1/Rgravity and scalar-tensor gravity.Physics Letters B, 575(1):1–3, 2003

    2003

  80. [88]

    Gravity stabilizes itself.The European Physical Journal C, 77(3):166, 2017

    Sumanta Chakraborty and Soumitra SenGupta. Gravity stabilizes itself.The European Physical Journal C, 77(3):166, 2017

    2017

  81. [89]

    Carl Brans and Robert H. Dicke. Mach’s principle and a relativistic theory of gravitation. Physical Review, 124(3):925, 1961

    1961

  82. [90]

    Solving higher curvature gravity theories.The European Physical Journal C, 76(10):552, 2016

    Sumanta Chakraborty and Soumitra SenGupta. Solving higher curvature gravity theories.The European Physical Journal C, 76(10):552, 2016

    2016

  83. [92]

    Mavromatos, John Rizos, Kyriakos Tamvakis, and Elizabeth Winstan- ley

    Panagiota Kanti, Nick E. Mavromatos, John Rizos, Kyriakos Tamvakis, and Elizabeth Winstan- ley. Dilatonic black holes in higher curvature string gravity.Physical Review D, 54(8):5049–5058, 1996

    1996

  84. [93]

    Odintsov

    Shin’ichi Nojiri and Sergei D. Odintsov. Modified gauss-bonnet theory as gravitational alterna- tive for dark energy.Physics Letters B, 631(1):1–6, 2005

    2005

  85. [94]

    Observation of gravitational waves from a binary black hole merger

    et al Abbott, Benjamin P. Observation of gravitational waves from a binary black hole merger. Physical review letters, 116(6):061102, 2016. 69

    2016

  86. [95]

    Lensing efficiency for gravitational wave mergers.Monthly Notices of the Royal Astronomical Society, 492(3):3359–3363, 2020

    O Contigiani. Lensing efficiency for gravitational wave mergers.Monthly Notices of the Royal Astronomical Society, 492(3):3359–3363, 2020

    2020

  87. [96]

    Probing the theory of gravity with gravitational lensing of gravitational waves and galaxy surveys.Monthly Notices of the Royal Astronomical Society, 494(2):1956–1970, 2020

    Suvodip Mukherjee, Benjamin D Wandelt, and Joseph Silk. Probing the theory of gravity with gravitational lensing of gravitational waves and galaxy surveys.Monthly Notices of the Royal Astronomical Society, 494(2):1956–1970, 2020

    1956

  88. [97]

    The gravity field of a particle.Proceedings of the Royal Society of London

    Charles Galton Darwin. The gravity field of a particle.Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 249(1257):180–194, 1959

    1959

  89. [98]

    On light tracks near a very massive star.Astronomical Journal, Vol

    Robert d’Escourt Atkinson. On light tracks near a very massive star.Astronomical Journal, Vol. 70, p. 517, 70:517, 1965

    1965

  90. [99]

    Strong lensing effect and quasinormal modes of oscillations of black holes inf(R, T) gravity theory

    Gayatri Mohan, Ronit Karmakar, Rupam Jyoti Borah, and Umananda Dev Goswami. Strong lensing effect and quasinormal modes of oscillations of black holes inf(R, T) gravity theory. arXiv preprint arXiv:2503.08402, 2025

    2025 arXiv

  91. [100]

    Cunningham and James M

    Christopher T. Cunningham and James M. Bardeen. The Optical Appearance of a Star Orbiting an Extreme Kerr Black Hole.The Astrophysical Journal, 183:237–264, 1973

    1973

  92. [101]

    Viewing the shadow of the black hole at the galac- ticcenter.The Astrophysical Journal, 528(1):L13, 1999

    Heino Falcke, Fulvio Melia, and Eric Agol. Viewing the shadow of the black hole at the galac- ticcenter.The Astrophysical Journal, 528(1):L13, 1999

    1999

  93. [102]

    Firouzjaee

    Mohsen Khodadi, Sunny Vagnozzi, and Javad T. Firouzjaee. Event Horizon Telescope obser- vations exclude compact objects in baseline mimetic gravity.Scientific Reports, 14(1):26932, 2024

    2024

  94. [103]

    Alireza Allahyari, Mohsen Khodadi, Sunny Vagnozzi, and David F. Mota. Magnetically charged black holes from non-linear electrodynamics and the Event Horizon Telescope.Journal of Cos- mology and Astroparticle Physics,, 02:003, 2020

    2020

  95. [104]

    Odintsov

    Shin’ichi Nojiri and Sergei D. Odintsov. Improving mimetic gravity with non-trivial scalar potential: Cosmology, black holes, shadow and photon sphere.Physics of the Dark Universe, 46:101669, 2024

    2024

  96. [105]

    Parameter estimation of hairy kerr black holes from its shadow and constraints from M87 ∗.Monthly Notices of the Royal Astronomical Society, 504(4):5927–5940, 2021

    Misba Afrin, Rahul Kumar, and Sushant G Ghosh. Parameter estimation of hairy kerr black holes from its shadow and constraints from M87 ∗.Monthly Notices of the Royal Astronomical Society, 504(4):5927–5940, 2021

    2021

  97. [106]

    Mohsen Khodadi, Gaetano Lambiase, and David F. Mota. No-hair theorem in the wake of Event Horizon Telescope.Journal of Cosmology and Astroparticle Physics,, 09:028, 2021

    2021

  98. [107]

    Testing horndeski gravity from eht observational results for rotating black holes.The Astrophysical Journal, 932(1):51, 2022

    Misba Afrin and Sushant G Ghosh. Testing horndeski gravity from eht observational results for rotating black holes.The Astrophysical Journal, 932(1):51, 2022

    2022

  99. [108]

    Probing Lorentz symmetry violation using the first image of Sagittarius A*: Constraints on standard-model extension coefficients.Physical Review 70 D, 106(10):104050, 2022

    Mohsen Khodadi and Gaetano Lambiase. Probing Lorentz symmetry violation using the first image of Sagittarius A*: Constraints on standard-model extension coefficients.Physical Review 70 D, 106(10):104050, 2022

    2022

  100. [109]

    Ghosh, and Anzhong Wang

    Rahul Kumar, Sushant G. Ghosh, and Anzhong Wang. Gravitational deflection of light and shadow cast by rotating Kalb-Ramond black holes.Physical Review D, 101(10):104001, 2020

    2020

  101. [110]

    Tests of loop quantum gravity from the event horizon telescope results of Sgr A ∗.The Astrophysical Journal, 944(2):149, 2023

    Misba Afrin, Sunny Vagnozzi, and Sushant G Ghosh. Tests of loop quantum gravity from the event horizon telescope results of Sgr A ∗.The Astrophysical Journal, 944(2):149, 2023

    2023

  102. [111]

    Eht observables as a tool to estimate parameters of su- permassive black holes.Monthly Notices of the Royal Astronomical Society, 524(3):3683–3691, 2023

    Misba Afrin and Sushant G Ghosh. Eht observables as a tool to estimate parameters of su- permassive black holes.Monthly Notices of the Royal Astronomical Society, 524(3):3683–3691, 2023

    2023

  103. [112]

    Gravitational lensing by a black hole in effective loop quantum gravity.Physical Review D, 105(6):064020, 2022

    Qi-Ming Fu and Xin Zhang. Gravitational lensing by a black hole in effective loop quantum gravity.Physical Review D, 105(6):064020, 2022

    2022

  104. [113]

    An upper limit on the charge of the black hole Sgr A ∗ from eht observations.The Astrophysical Journal, 944(2):174, 2023

    Sushant G Ghosh and Misba Afrin. An upper limit on the charge of the black hole Sgr A ∗ from eht observations.The Astrophysical Journal, 944(2):174, 2023

    2023

  105. [114]

    Hunting for extra dimensions in the shadow of M87 ∗

    Sunny Vagnozzi and Luca Visinelli. Hunting for extra dimensions in the shadow of M87 ∗. Physical Review D, 100(2):024020, 2019

    2019

  106. [115]

    Shadow of slowly rotating Kalb-Ramond black holes

    Wentao Liu, Di Wu, and Jieci Wang. Shadow of slowly rotating Kalb-Ramond black holes. Journal of Cosmology and Astroparticle Physics,, 05:017, 2025

    2025

  107. [116]

    Shin’ichi Nojiri and S. D. Odintsov. Black holes and their shadows inF(R) gravity.Physics of the Dark Universe, 47:101785, 2025

    2025

  108. [117]

    Shin’ichi Nojiri and S. D. Odintsov. Black holes, photon sphere, and cosmology in ghost-free f(G) gravity.Physics of the Dark Universe, 46:101702, 2024

    2024

  109. [118]

    Testing the rotational nature of the supermassive object M87 ∗ from the circularity and size of its first image.Physical Review D, 100(4):044057, 2019

    Cosimo Bambi, Katherine Freese, Sunny Vagnozzi, and Luca Visinelli. Testing the rotational nature of the supermassive object M87 ∗ from the circularity and size of its first image.Physical Review D, 100(4):044057, 2019

    2019

  110. [119]

    Ghosh, and Anzhong Wang

    Misba Afrin, Sushant G. Ghosh, and Anzhong Wang. Testing EGB gravity coupled to bumblebee field and black hole parameter estimation with EHT observations.Physics of the Dark Universe, 46:101642, 2024

    2024

  111. [120]

    Schwarzschild black hole lensing.Physical Review D, 62(8):084003, 2000

    Kumar Shwetketu Virbhadra and George FR Ellis. Schwarzschild black hole lensing.Physical Review D, 62(8):084003, 2000

    2000

  112. [121]

    Theoretical gravitational lensing–beyond the weak-field small-angle approxima- tion

    Volker Perlick. Theoretical gravitational lensing–beyond the weak-field small-angle approxima- tion. InThe Eleventh Marcel Grossmann Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes), ...

    2008

  113. [122]

    Strong field limit of black hole gravitational lensing.General Relativity and Gravitation, 33:1535–1548, 2001

    Valerio Bozza, Salvatore Capozziello, Gerardo Iovane, and Gaetano Scarpetta. Strong field limit of black hole gravitational lensing.General Relativity and Gravitation, 33:1535–1548, 2001. 71

    2001

  114. [123]

    Gravitational lensing in the strong field limit.Physical Review D, 66(10):103001, 2002

    Valerio Bozza. Gravitational lensing in the strong field limit.Physical Review D, 66(10):103001, 2002

    2002

  115. [124]

    Spacetime perspective of schwarzschild lensing.Physical Review D, 61(6):064021, 2000

    Simonetta Frittelli, Thomas P Kling, and Ezra T Newman. Spacetime perspective of schwarzschild lensing.Physical Review D, 61(6):064021, 2000

    2000

  116. [125]

    The strong gravitational lens finding challenge.Astronomy & Astrophysics, 625:A119, 2019

    R Benton Metcalf, MASSIMO Meneghetti, Camille Avestruz, Fabio Bellagamba, Cl´ ecio R Bom, Emmanuel Bertin, R´ emi Cabanac, F Courbin, Andrew Davies, Etienne Decenci` ere, et al. The strong gravitational lens finding challenge.Astronomy & Astrophysics, 625:A119, 2019

    2019

  117. [126]

    Strong gravitational lensing of gravitational waves: A review.Universe, 9(5):200, 2023

    Margherita Grespan and Marek Biesiada. Strong gravitational lensing of gravitational waves: A review.Universe, 9(5):200, 2023

    2023

  118. [127]

    Strong gravitational lensing and shadow constraint from M87∗ of slowly rotating kerr-like black hole.Annals of Physics, 447:169147, 2022

    Xiao-Mei Kuang and Ali ¨Ovg¨ un. Strong gravitational lensing and shadow constraint from M87∗ of slowly rotating kerr-like black hole.Annals of Physics, 447:169147, 2022

    2022

  119. [128]

    Testing dynamical torsion effects on the charged black hole’s shadow, deflection angle and greybody with M87 ∗ and Sgr A ∗ from eht.Annals of Physics, 448:169197, 2023

    Reggie C Pantig and Ali ¨Ovg¨ un. Testing dynamical torsion effects on the charged black hole’s shadow, deflection angle and greybody with M87 ∗ and Sgr A ∗ from eht.Annals of Physics, 448:169197, 2023

    2023

  120. [129]

    Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem

    Ali ¨Ovg¨ un. Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem. Physical Review D, 98(4):044033, 2018

    2018

  121. [130]

    Strong gravitational lensing—a probe for extra dimensions and kalb-ramond field.Journal of Cosmology and Astroparticle Physics, 2017(07):045, 2017

    Sumanta Chakraborty and Soumitra SenGupta. Strong gravitational lensing—a probe for extra dimensions and kalb-ramond field.Journal of Cosmology and Astroparticle Physics, 2017(07):045, 2017

    2017

  122. [131]

    A Ara´ ujo Filho

    A. A Ara´ ujo Filho. Antisymmetric tensor influence on charged black hole lensing phenomena and time delay.Journal of High Energy Astrophysics, page 100401, 2025

    2025

  123. [132]

    Gravitational lensing by scalar-tensor wormholes and the energy conditions.Physical Review D, 96(4):044037, 2017

    Rajibul Shaikh and Sayan Kar. Gravitational lensing by scalar-tensor wormholes and the energy conditions.Physical Review D, 96(4):044037, 2017

    2017

  124. [133]

    A Ara´ ujo Filho, J

    A. A Ara´ ujo Filho, J. R Nascimento, A. Yu Petrov, and P. J Porf ´ ırio. Gravitational lensing by a lorentz-violating black hole.arXiv preprint arXiv:2404.04176, 2024

    2024

  125. [134]

    A Ara´ ujo Filho, J Kriz, S Zare, and PJ Porf ´ ırio

    N Heidari, H Hassanabadi, A. A Ara´ ujo Filho, J Kriz, S Zare, and PJ Porf ´ ırio. Gravitational signatures of a non–commutative stable black hole.Physics of the Dark Universe, page 101382, 2023

    2023

  126. [135]

    Exact traversable wormhole solution in bumblebee gravity.Physical Review D, 99(2):024042, 2019

    Ali ¨Ovg¨ un, Kimet Jusufi, and˙Izzet Sakallı. Exact traversable wormhole solution in bumblebee gravity.Physical Review D, 99(2):024042, 2019

    2019

  127. [136]

    Can we distinguish between black holes and wormholes by their einstein-ring systems?Physical Review D, 86(10):104062, 2012

    Naoki Tsukamoto, Tomohiro Harada, and Kohji Yajima. Can we distinguish between black holes and wormholes by their einstein-ring systems?Physical Review D, 86(10):104062, 2012

    2012

  128. [137]

    Strong gravitational lensing by wormholes.Journal of Cosmology and Astroparticle Physics,, 2019(07):028, 2019

    Rajibul Shaikh, Pritam Banerjee, Suvankar Paul, and Tapobrata Sarkar. Strong gravitational lensing by wormholes.Journal of Cosmology and Astroparticle Physics,, 2019(07):028, 2019. 72

    2019

  129. [138]

    The application of weierstrass elliptic functions to schwarzschild null geodesics.Classical and Quantum Gravity, 29(6):065016, 2012

    Gary W Gibbons and Martin Vyska. The application of weierstrass elliptic functions to schwarzschild null geodesics.Classical and Quantum Gravity, 29(6):065016, 2012

    2012

  130. [139]

    Retrolensing by a wormhole at deflection anglesπand 3π.Physical Review D, 95(8):084021, 2017

    Naoki Tsukamoto. Retrolensing by a wormhole at deflection anglesπand 3π.Physical Review D, 95(8):084021, 2017

    2017

  131. [140]

    Lobo, Martin G

    Iarley P. Lobo, Martin G. Richarte, J. P. Morais Gra¸ ca, and H. Moradpour. Thin-shell wormholes in Rastall gravity.Eur. Phys. J. Plus, 135(7):550, 2020

    2020

  132. [141]

    Strong deflection limit analysis and gravitational lensing of an ellis wormhole

    Naoki Tsukamoto. Strong deflection limit analysis and gravitational lensing of an ellis wormhole. Physical Review D, 94(12):124001, 2016

    2016

  133. [142]

    Conservation of distortion of gravitationally lensed images.Physical Review D, 109(12):124004, 2024

    KS Virbhadra. Conservation of distortion of gravitationally lensed images.Physical Review D, 109(12):124004, 2024

    2024

  134. [143]

    R. A. Konoplya and A. Zhidenko. Decay of a charged scalar and Dirac fields in the Kerr- Newman-de Sitter background.Physical Review D, 76(8):084018, 2007. [Erratum: Phys.Rev.D 90, 029901 (2014)]

    2007

  135. [144]

    R. A. Konoplya and A. Zhidenko. Massive charged scalar field in the Kerr-Newman background I: quasinormal modes, late-time tails and stability.Physical Review D, 88:024054, 2013

    2013

  136. [145]

    Quasinormal modes, thermodynamics and shadow of black holes in Hu–Sawickif(R) gravity theory.The European Physical Journal C, 84(9):969, 2024

    Ronit Karmakar and Umananda Dev Goswami. Quasinormal modes, thermodynamics and shadow of black holes in Hu–Sawickif(R) gravity theory.The European Physical Journal C, 84(9):969, 2024

    2024

  137. [146]

    Higher order wkb formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations.Classical and Quantum Gravity, 36(15):155002, 2019

    RA Konoplya, A Zhidenko, and AF Zinhailo. Higher order wkb formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations.Classical and Quantum Gravity, 36(15):155002, 2019

    2019

  138. [147]

    Quasinormal modes and thermodynamic properties of gup-corrected schwarzschild black hole surrounded by quintessence

    Ronit Karmakar, Dhruba Jyoti Gogoi, and Umananda Dev Goswami. Quasinormal modes and thermodynamic properties of gup-corrected schwarzschild black hole surrounded by quintessence. International Journal of Modern Physics A, 37(28n29):2250180, 2022

    2022

  139. [148]

    Quasinormal modes of black holes: From astro- physics to string theory.Reviews of Modern Physics, 83(3):793–836, 2011

    Roman A Konoplya and Alexander Zhidenko. Quasinormal modes of black holes: From astro- physics to string theory.Reviews of Modern Physics, 83(3):793–836, 2011

    2011

  140. [149]

    K. D. Kokkotas, R. A. Konoplya, and A. Zhidenko. Quasinormal modes, scattering and Hawking radiation of Kerr-Newman black holes in a magnetic field.Physical Review D, 83:024031, 2011

    2011

  141. [150]

    Connection Between the Shadow Radius and Quasinormal Modes in Rotating Spacetimes.Physical Review D, 101(12):124063, 2020

    Kimet Jusufi. Connection Between the Shadow Radius and Quasinormal Modes in Rotating Spacetimes.Physical Review D, 101(12):124063, 2020

    2020

  142. [151]

    Correspondence between grey-body factors and quasinormal frequencies for rotating black holes.Physics Letters B, 861:139288, 2025

    RA Konoplya and A Zhidenko. Correspondence between grey-body factors and quasinormal frequencies for rotating black holes.Physics Letters B, 861:139288, 2025

    2025

  143. [152]

    R. A. Konoplya and A. Zhidenko. Correspondence between grey-body factors and quasinormal modes.Journal of Cosmology and Astroparticle Physics,, 09:068, 2024. 73

    2024

  144. [153]

    Springer, 2024

    Nicola Franchini and Sebastian H V¨ olkel.Testing general relativity with black hole quasi-normal modes, pages 361–416. Springer, 2024

    2024

  145. [154]

    Quantum oppenheimer-snyder and swiss cheese models.Physical Review Letters, 130(10):101501, 2023

    Jerzy Lewandowski, Yongge Ma, Jinsong Yang, and Cong Zhang. Quantum oppenheimer-snyder and swiss cheese models.Physical Review Letters, 130(10):101501, 2023

    2023

  146. [155]

    Circular orbits and accre- tion disk around a deformed-Schwarzschild black hole in loop quantum gravity.Physics of the Dark Universe, 49:102027, 2025

    Kourosh Nozari, Sara Saghafi, Milad Hajebrahimi, and Kimet Jusufi. Circular orbits and accre- tion disk around a deformed-Schwarzschild black hole in loop quantum gravity.Physics of the Dark Universe, 49:102027, 2025

    2025

  147. [156]

    Black-hole normal modes: A wkb approach

    Sai Iyer and Clifford M Will. Black-hole normal modes: A wkb approach. i. foundations and application of a higher-order wkb analysis of potential-barrier scattering.Physical Review D, 35(12):3621, 1987

    1987

  148. [157]

    Black-hole normal modes: A wkb approach

    Sai Iyer. Black-hole normal modes: A wkb approach. ii. schwarzschild black holes.Physical Review D, 35(12):3632, 1987

    1987

  149. [158]

    Quasinormal behavior of the d-dimensional schwarzschild black hole and the higher order wkb approach.Physical Review D, 68(2):024018, 2003

    RA Konoplya. Quasinormal behavior of the d-dimensional schwarzschild black hole and the higher order wkb approach.Physical Review D, 68(2):024018, 2003

    2003

  150. [159]

    Oxford university press, 1998

    Subrahmanyan Chandrasekhar.The mathematical theory of black holes, volume 69. Oxford university press, 1998

    1998

  151. [160]

    A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes.Journal of Cosmology and Astroparticle Physics,, 07:066, 2020

    Mariam Bouhmadi-L´ opez, Suddhasattwa Brahma, Che-Yu Chen, Pisin Chen, and Dong-han Yeom. A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes.Journal of Cosmology and Astroparticle Physics,, 07:066, 2020

    2020

  152. [161]

    Koussour

    Dhruba Jyoti Gogoi, Ali ¨Ovg¨ un, and M. Koussour. Quasinormal modes of black holes in f(Q) gravity.The European Physical Journal C, 83(8):700, 2023

    2023

  153. [162]

    Expansion formulas and addition theo- rems for gegenbauer functions.Journal of Mathematical Physics, 17(11):1933–1948, 1976

    Loyal Durand, Paul M Fishbane, and LM Simmons Jr. Expansion formulas and addition theo- rems for gegenbauer functions.Journal of Mathematical Physics, 17(11):1933–1948, 1976

    1933

  154. [163]

    Gegenbauer polynomials and bi- univalent functions.Palestine Journal of Mathematics, 10(2):625–632, 2021

    Ala Amourah, A Alamoush, and Mohammad Al-Kaseasbeh. Gegenbauer polynomials and bi- univalent functions.Palestine Journal of Mathematics, 10(2):625–632, 2021

    2021

  155. [164]

    Inequalities for legendre functions and gegenbauer functions.Journal of approx- imation theory, 64(2):226–234, 1991

    Georg Loh¨ ofer. Inequalities for legendre functions and gegenbauer functions.Journal of approx- imation theory, 64(2):226–234, 1991

    1991

  156. [165]

    On a generalization of the generating function for gegenbauer polynomials

    Howard S Cohl. On a generalization of the generating function for gegenbauer polynomials. Integral Transforms and special functions, 24(10):807–816, 2013

    2013

  157. [166]

    Asymptotics of the generalized gegenbauer functions of fractional degree.Journal of Approximation Theory, 253:105378, 2020

    Wenjie Liu and Li-Lian Wang. Asymptotics of the generalized gegenbauer functions of fractional degree.Journal of Approximation Theory, 253:105378, 2020

    2020

  158. [167]

    Quantum extension of the kruskal spacetime.Physical Review D, 98(12):126003, 2018

    Abhay Ashtekar, Javier Olmedo, and Parampreet Singh. Quantum extension of the kruskal spacetime.Physical Review D, 98(12):126003, 2018

    2018

  159. [168]

    Quantum transfiguration of kruskal 74 black holes.Physical review letters, 121(24):241301, 2018

    Abhay Ashtekar, Javier Olmedo, and Parampreet Singh. Quantum transfiguration of kruskal 74 black holes.Physical review letters, 121(24):241301, 2018

    2018

  160. [170]

    Anshuman Baruah, Yassine Sekhmani, Sunil Kumar Maurya, Atri Deshamukhya, and Mah- mood Khalid Jasim. Quasinormal modes, greybody factors, and Hawking radiation sparsity of black holes influenced by a global monopole charge in Kalb-Ramond gravity.Journal of Cosmology and Astrop...

    2025

  161. [171]

    Gravitational perturbations of nonsingular black holes in confor- mal gravity.Physical Review D, 99(10):104003, 2019

    Che-Yu Chen and Pisin Chen. Gravitational perturbations of nonsingular black holes in confor- mal gravity.Physical Review D, 99(10):104003, 2019

    2019

  162. [172]

    A Ara´ ujo Filho

    A. A Ara´ ujo Filho. How does non-metricity affect particle creation and evaporation in bumblebee gravity?Journal of Cosmology and Astroparticle Physics, 2025(06):026, 2025

    2025

  163. [173]

    An approach to gravitational radiation by a method of spin coefficients.Journal of Mathematical Physics, 3(3):566–578, 1962

    Ezra Newman and Roger Penrose. An approach to gravitational radiation by a method of spin coefficients.Journal of Mathematical Physics, 3(3):566–578, 1962

    1962

  164. [174]

    The mathematical theory of black holes

    Subrahmanijan Chandrasekhar. The mathematical theory of black holes. InGeneral Relativity and Gravitation: Invited Papers and Discussion Reports of the 10th International Conference on General Relativity and Gravitation, Padua, July 3–8, 1983, pages 5–26. Springer, 1984

    1983

  165. [175]

    Saulo Albuquerque, Iarley P Lobo, and Valdir B Bezerra. Massless dirac perturbations in a consistent model of loop quantum gravity black hole: quasinormal modes and particle emission rates.Classical and Quantum Gravity, 40(17):174001, 2023

    2023

  166. [176]

    Massless dirac perturbations of black holes in f (q) gravity: quasinormal modes and a weak deflection angle.Communications in Theoretical Physics, 76(9):095403, 2024

    Ahmad Al-Badawi and Sohan Kumar Jha. Massless dirac perturbations of black holes in f (q) gravity: quasinormal modes and a weak deflection angle.Communications in Theoretical Physics, 76(9):095403, 2024

    2024

  167. [177]

    Hawk- ing radiation by spherically-symmetric static black holes for all spins: Teukolsky equations and potentials.Physical Review D, 103(10):104010, 2021

    Alexandre Arbey, J´ er´ emy Auffinger, Marc Geiller, Etera R Livine, and Francesco Sartini. Hawk- ing radiation by spherically-symmetric static black holes for all spins: Teukolsky equations and potentials.Physical Review D, 103(10):104010, 2021

    2021

  168. [178]

    Saraswati Devi, Rittick Roy, and Sayan Chakrabarti. Quasinormal modes and greybody factors of the novel four dimensional gauss–bonnet black holes in asymptotically de sitter space time: scalar, electromagnetic and dirac perturbations.The European Physical Journal C, 80(8):760, 2020

    2020

  169. [179]

    Price, and Jorge Pullin

    Carsten Gundlach, Richard H. Price, and Jorge Pullin. Late time behavior of stellar collapse and explosions: 1. Linearized perturbations.Physical Review D, 49:883–889, 1994

    1994

  170. [180]

    Ringing of extreme regular black holes.Gravitation and Cosmology, 30(3):279–288, 2024

    Milena Skvortsova. Ringing of extreme regular black holes.Gravitation and Cosmology, 30(3):279–288, 2024

    2024

  171. [181]

    S. V. Bolokhov. Late time decay of scalar and Dirac fields around an asymptotically de Sit- 75 ter black hole in the Euler–Heisenberg electrodynamics.The European Physical Journal C, 84(6):634, 2024

    2024

  172. [182]

    Quasinormal modes and greybody factor of a Lorentz- violating black hole.Journal of Cosmology and Astroparticle Physics,, 07:008, 2024

    Wen-Di Guo, Qin Tan, and Yu-Xiao Liu. Quasinormal modes and greybody factor of a Lorentz- violating black hole.Journal of Cosmology and Astroparticle Physics,, 07:008, 2024

    2024

  173. [183]

    Echoes of massless scalar field induced from hairy schwarzschild black hole.Physics Letters B, 853:138688, 2024

    Zhen-Hao Yang, Cheng Xu, Xiao-Mei Kuang, Bin Wang, and Rui-Hong Yue. Echoes of massless scalar field induced from hairy schwarzschild black hole.Physics Letters B, 853:138688, 2024

    2024

  174. [184]

    Quasinormal modes and bounding greybody factors of GUP-corrected black holes in Kalb–Ramond gravity.Annals of Physics, 455:169393, 2023

    Anshuman Baruah, Ali ¨Ovg¨ un, and Atri Deshamukhya. Quasinormal modes and bounding greybody factors of GUP-corrected black holes in Kalb–Ramond gravity.Annals of Physics, 455:169393, 2023

    2023

  175. [185]

    Cai-Ying Shao, Cong Zhang, Wei Zhang, and Cheng-Gang Shao. Scalar fields around a loop quantum gravity black hole in de Sitter spacetime: Quasinormal modes, late-time tails and strong cosmic censorship.Physical Review D, 109(6):064012, 2024

    2024

  176. [186]

    Thermodynamics and shadows of quantum-corrected reissner– nordstr¨ om black hole surrounded by quintessence.Physics of the Dark Universe, 42:101293, 2023

    Bilel Hamil and BC L¨ utf¨ uo˘ glu. Thermodynamics and shadows of quantum-corrected reissner– nordstr¨ om black hole surrounded by quintessence.Physics of the Dark Universe, 42:101293, 2023

    2023

  177. [187]

    Charged black holes with yukawa potential.Physics of the Dark Universe, 46:101711, 2024

    Adailton Azevedo Ara´ ujo Filho, Kimet Jusufi, Bertha Cuadros-Melgar, Genly Leon, Abdul Jawad, and CE Pellicer. Charged black holes with yukawa potential.Physics of the Dark Universe, 46:101711, 2024

    2024

  178. [188]

    The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions.Nuclear Physics B, 974:115639, 2022

    Xiao-Xiong Zeng, Guo-Ping Li, and Ke-Jian He. The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions.Nuclear Physics B, 974:115639, 2022

    2022

  179. [189]

    A Ara´ ujo Filho

    A. A Ara´ ujo Filho. Remarks on a nonlinear electromagnetic extension in ads reissner-nordstr¨ om spacetime.Journal of Cosmology and Astroparticle Physics, 2025(01):072, 2025

    2025

  180. [190]

    First M87∗ event horizon telescope results

    David Ball, Chi-kwan Chan, Pierre Christian, Buell T Jannuzi, Junhan Kim, Daniel P Marrone, Lia Medeiros, Feryal Ozel, Dimitrios Psaltis, Mel Rose, et al. First M87∗ event horizon telescope results. i. the shadow of the supermassive black hole.The Astrophysical Journal Letters, 2019

    2019

  181. [191]

    Can the eht M87 ∗ results be used to test general relativity.Physical Review D, 103(2):024023, 2021

    Samuel E Gralla. Can the eht M87 ∗ results be used to test general relativity.Physical Review D, 103(2):024023, 2021

    2021

  182. [192]

    First M87∗ event horizon telescope results

    Kazunori Akiyama, Antxon Alberdi, Walter Alef, Keiichi Asada, Rebecca Azulay, Anne-Kathrin Baczko, David Ball, Mislav Balokovi´ c, John Barrett, Dan Bintley, et al. First M87∗ event horizon telescope results. v. physical origin of the asymmetric ring.The Astrophysical Journal ...

    2019

  183. [193]

    First sagittarius 76 a* event horizon telescope results

    Kazunori Akiyama, Antxon Alberdi, Walter Alef, Juan Carlos Algaba, Richard Anantua, Keiichi Asada, Rebecca Azulay, Uwe Bach, Anne-Kathrin Baczko, David Ball, et al. First sagittarius 76 a* event horizon telescope results. iv. variability, morphology, and black hole mass.The As...

    2022

  184. [194]

    First sagittarius a* event horizon telescope results

    Kazunori Akiyama, Antxon Alberdi, Walter Alef, Juan Carlos Algaba, Richard Anantua, Keiichi Asada, Rebecca Azulay, Uwe Bach, Anne-Kathrin Baczko, David Ball, et al. First sagittarius a* event horizon telescope results. vi. testing the black hole metric.The Astrophysical Journa...

    2022

  185. [195]

    Calculating black hole shadows: Review of analytical studies.Physics Reports, 947:1–39, 2022

    Volker Perlick and Oleg Yu Tsupko. Calculating black hole shadows: Review of analytical studies.Physics Reports, 947:1–39, 2022

    2022

  186. [196]

    Rotating black holes in 4d einstein-gauss-bonnet gravity and its shadow.Journal of Cosmology and Astroparticle Physics, 2020(07):053, 2020

    Rahul Kumar and Sushant G Ghosh. Rotating black holes in 4d einstein-gauss-bonnet gravity and its shadow.Journal of Cosmology and Astroparticle Physics, 2020(07):053, 2020

    2020

  187. [197]

    Optical appearance and shadow of kalb–ramond black hole: effects of plasma and accretion models.The European Physical Journal C, 85(6):676, 2025

    Mou Xu, Ruonan Li, Jianbo Lu, Shining Yang, and Shu-Min Wu. Optical appearance and shadow of kalb–ramond black hole: effects of plasma and accretion models.The European Physical Journal C, 85(6):676, 2025

    2025

  188. [198]

    Effect of quintessence dark energy on the shadow of hayward black holes with spherical accretion.Indian Journal of Physics, 98(8):3019–3032, 2024

    Malihe Heydari-Fard. Effect of quintessence dark energy on the shadow of hayward black holes with spherical accretion.Indian Journal of Physics, 98(8):3019–3032, 2024

    2024

  189. [199]

    The acs fornax cluster survey

    John P Blakeslee, Andr´ es Jord´ an, Simona Mei, Patrick Cˆ ot´ e, Laura Ferrarese, Leopoldo Infante, Eric W Peng, John L Tonry, and Michael J West. The acs fornax cluster survey. v. measure- ment and recalibration of surface brightness fluctuations and a precise value of the ...

    2009

  190. [200]

    The black hole mass in M87 ∗ from gemini/nifs adaptive optics observations.The Astrophysical Journal, 729(2):119, 2011

    Karl Gebhardt, Joshua Adams, Douglas Richstone, Tod R Lauer, SM Faber, Kayhan G¨ ultekin, Jeremy Murphy, and Scott Tremaine. The black hole mass in M87 ∗ from gemini/nifs adaptive optics observations.The Astrophysical Journal, 729(2):119, 2011

    2011

  191. [201]

    The inner halo of M87 ∗: a first direct view of the red-giant population.Astronomy & Astrophysics, 524:A71, 2010

    Sarah Bird, William E Harris, John P Blakeslee, and Chris Flynn. The inner halo of M87 ∗: a first direct view of the red-giant population.Astronomy & Astrophysics, 524:A71, 2010

    2010

  192. [202]

    First M87∗ event horizon telescope results

    Kazunori Akiyama, Antxon Alberdi, Walter Alef, Keiichi Asada, Rebecca Azulay, Anne-Kathrin Baczko, David Ball, Mislav Balokovi´ c, John Barrett, Dan Bintley, et al. First M87∗ event horizon telescope results. vi. the shadow and mass of the central black hole.The Astrophysical ...

    2019

  193. [203]

    Mass distribution in the galactic center based on interferometric astrometry of multiple stellar orbits.Astronomy & Astrophysics, 657:L12, 2022

    R Abuter, N Aimar, A Amorim, J Ball, M Baub¨ ock, JP Berger, H Bonnet, G Bourdarot, W Brandner, V Cardoso, et al. Mass distribution in the galactic center based on interferometric astrometry of multiple stellar orbits.Astronomy & Astrophysics, 657:L12, 2022

    2022

  194. [204]

    Detection of the schwarzschild precession in the orbit of the star s2 near the galactic centre massive black hole.Astronomy & Astrophysics, 636:L5, 2020

    R Abuter, A Amorim, M Baub¨ ock, JP Berger, H Bonnet, W Brandner, V Cardoso, Y Cl´ enet, PT De Zeeuw, J Dexter, et al. Detection of the schwarzschild precession in the orbit of the star s2 near the galactic centre massive black hole.Astronomy & Astrophysics, 636:L5, 2020. 77

    2020

  195. [205]

    Do shadows of Sgr A ∗ and M87 ∗ indicate black holes with a magnetic monopole charge?arXiv preprint arXiv:2207.06034, 2022

    Indrani Banerjee, Subhadip Sau, and Soumitra SenGupta. Do shadows of Sgr A ∗ and M87 ∗ indicate black holes with a magnetic monopole charge?arXiv preprint arXiv:2207.06034, 2022

    2022 arXiv

  196. [206]

    G. W. Gibbons and M. C. Werner. Applications of the Gauss-Bonnet theorem to gravitational lensing.Classical and Quantum Gravity, 25:235009, 2008

    2008

  197. [207]

    Geometric approach to circular photon orbits and black hole shadows.Physical Review D, 106(2):L021501, 2022

    Chen-Kai Qiao and Ming Li. Geometric approach to circular photon orbits and black hole shadows.Physical Review D, 106(2):L021501, 2022

    2022

  198. [208]

    Heidari, A

    N. Heidari, A. A. Ara´ ujo Filho, and Iarley P. Lobo. Non-commutativity in Hayward spacetime. 3 2025

    2025

  199. [209]

    Curvatures, photon spheres, and black hole shadows.Physical Review D, 106(8):084060, 2022

    Chen-Kai Qiao. Curvatures, photon spheres, and black hole shadows.Physical Review D, 106(8):084060, 2022

    2022

  200. [210]

    A Ara´ ujo Filho, N Heidari, J

    A. A Ara´ ujo Filho, N Heidari, J. A. A. S Reis, and H Hassanabadi. The impact of an antisym- metric tensor on charged black holes: evaporation process, geodesics, deflection angle, scattering effects and quasinormal modes.Classical and Quantum Gravity, 42(6):065026, 2025

    2025

  201. [211]

    The existence and distribution of photon spheres near spherically symmetric black holes–a geometric analysis.arXiv preprint arXiv:2407.14035, 2024

    Chen-Kai Qiao. The existence and distribution of photon spheres near spherically symmetric black holes–a geometric analysis.arXiv preprint arXiv:2407.14035, 2024

    2024 arXiv

  202. [212]

    A Ara´ ujo Filho

    A. A Ara´ ujo Filho. Analysis of a nonlinear electromagnetic generalization of the reissner– nordstr¨ om black hole.The European Physical Journal C, 85(4):454, 2025

    2025

  203. [213]

    A. A. Ara´ ujo Filho, N. Heidari, Iarley P. Lobo, and Yuxuan Shi. Optical Phenomena in a Non-Commutative Kalb-Ramond Black Hole Spacetime. 8 2025

    2025

  204. [214]

    A Ara´ ujo Filho, J

    A. A Ara´ ujo Filho, J. R Nascimento, A Yu Petrov, P. J Porf ´ ırio, and Ali ¨Ovg¨ un. Effects of non-commutative geometry on black hole properties.Physics of the Dark Universe, 46:101630, 2024

    2024

  205. [215]

    Gravitational signatures of a non- linear electrodynamics in f(R,T) gravity.Journal of Cosmology and Astroparticle Physics, 2025(09):015, 2025

    AA Ara´ ujo Filho, N Heidari, IP Lobo, and VB Bezerra. Gravitational signatures of a non- linear electrodynamics in f(R,T) gravity.Journal of Cosmology and Astroparticle Physics, 2025(09):015, 2025

    2025

  206. [216]

    A Ara´ ujo Filho, N Heidari, and Ali ¨Ovg¨ un

    A. A Ara´ ujo Filho, N Heidari, and Ali ¨Ovg¨ un. Geodesics, accretion disk, gravitational lensing, time delay, and effects on neutrinos induced by a non-commutative black hole.Journal of Cosmology and Astroparticle Physics, 2025(06):062, 2025

    2025

  207. [217]

    Heidari, A

    N. Heidari, A. A. Ara´ ujo Filho, R. C. Pantig, and A. ¨Ovg¨ un. Absorption, scattering, geodesics, shadows and lensing phenomena of black holes in effective quantum gravity.Physics of the Dark Universe, 47:101815, 2025

    2025

  208. [218]

    Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime.Physical Review D, 95(6):064035, 2017

    Naoki Tsukamoto. Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime.Physical Review D, 95(6):064035, 2017

    2017

  209. [219]

    Gravitational lensing in spherically symmetric static space- 78 times with centrifugal force reversal.Gen

    Wolfgang Hasse and Volker Perlick. Gravitational lensing in spherically symmetric static space- 78 times with centrifugal force reversal.Gen. Rel. Grav., 34:415–433, 2002

    2002

  210. [220]

    Quantum gravity phenomenology at the dawn of the multi-messenger era—a review.Progress in Particle and Nuclear Physics, 125:103948, 2022

    P Jetzer, J Alvarez-Muniz, R Alves Batista, G Amelino-Camelia, V Antonelli, M Arzano, M Asorey, JL Atteia, S Bahamonde, F Bajardi, et al. Quantum gravity phenomenology at the dawn of the multi-messenger era—a review.Progress in Particle and Nuclear Physics, 125:103948, 2022

    2022

  211. [221]

    Alves Batista et al

    R. Alves Batista et al. White paper and roadmap for quantum gravity phenomenology in the multi-messenger era.Classical and Quantum Gravity, 42(3):032001, 2025

    2025

  212. [222]

    Quantum-Spacetime Phenomenology.Living Rev

    Giovanni Amelino-Camelia. Quantum-Spacetime Phenomenology.Living Rev. Rel., 16:5, 2013

    2013

  213. [223]

    Casana, A

    R. Casana, A. Cavalcante, F. P. Poulis, and E. B. Santos. Exact Schwarzschild-like solution in a bumblebee gravity model.Physical Review D, 97(10):104001, 2018

    2018

  214. [224]

    Static and spherically symmetric black holes in gravity with a background Kalb-Ramond field.Physical Review D, 108(12):124004, 2023

    Ke Yang, Yue-Zhe Chen, Zheng-Qiao Duan, and Ju-Ying Zhao. Static and spherically symmetric black holes in gravity with a background Kalb-Ramond field.Physical Review D, 108(12):124004, 2023

    2023

  215. [225]

    Addison-Wesley, San Francisco, USA, 3rd edition, 2002

    Herbert Goldstein, Charles Poole, and John Safko.Classical Mechanics. Addison-Wesley, San Francisco, USA, 3rd edition, 2002

    2002

  216. [226]

    Improved determination ofγby vlbi.Astronomy & Astrophysics, 529:A70, 2011

    SB Lambert and Chr Le Poncin-Lafitte. Improved determination ofγby vlbi.Astronomy & Astrophysics, 529:A70, 2011

    2011

  217. [227]

    Irwin I. Shapiro. Fourth Test of General Relativity.Physical Review Letters, 13:789–791, 1964

    1964

  218. [228]

    Estimating the strength of Lorentzian distribution in non-commutative geometry by solar system tests

    Rui-Bo Wang, Shi-Jie Ma, Jian-Bo Deng, and Xian-Ru Hu. Estimating the strength of Lorentzian distribution in non-commutative geometry by solar system tests. 11 2024

    2024

  219. [229]

    Bertotti, L

    B. Bertotti, L. Iess, and P. Tortora. A test of general relativity using radio links with the Cassini spacecraft.Nature, 425:374–376, 2003

    2003

  220. [230]

    The confrontation between general relativity and experiment.Living reviews in relativity, 17(1):1–117, 2014

    Clifford M Will. The confrontation between general relativity and experiment.Living reviews in relativity, 17(1):1–117, 2014

    2014

  221. [231]

    A Ara´ ujo Filho, J Furtado, J

    A. A Ara´ ujo Filho, J Furtado, J. A. A. S Reis, and J. E. G Silva. Thermodynamical properties of an ideal gas in a traversable wormhole.Classical and Quantum Gravity, 40(24):245001, 2023

    2023

  222. [232]

    J Furtado, H Hassanabadi, J. A. A. S Reis, et al. Thermal analysis of photon-like particles in rainbow gravity.arXiv preprint arXiv:2305.08587, 2023

    2023 arXiv

  223. [233]

    A Ara´ ujo Filho and J

    A. A Ara´ ujo Filho and J. A. A. S Reis. How does geometry affect quantum gases?International Journal of Modern Physics A, 37(11n12):2250071, 2022

    2022

  224. [234]

    A Ara´ ujo Filho, J

    A. A Ara´ ujo Filho, J. A. A. S Reis, and Ali ¨Ovg¨ un. Modified particle dynamics and thermo- dynamics in a traversable wormhole in bumblebee gravity.The European Physical Journal C, 85(1):83, 2025

    2025

  225. [235]

    A Ara´ ujo Filho

    A. A Ara´ ujo Filho. Particle creation and evaporation in kalb-ramond gravity.Journal of Cos- 79 mology and Astroparticle Physics, 2025(04):076, 2025

    2025

  226. [236]

    A Ara´ ujo Filho

    A. A Ara´ ujo Filho. Particle production induced by a lorentzian non–commutative spacetime. Annals of Physics, page 170167, 2025

    2025

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Reviewed August 4, 2026 · model on record in the stance chip above.