Pith. sign in

REVIEW 4 major objections 4 minor 39 references

Graybody factors and absorption cross-sections of non-exchange black holes in Instein-coupled scalar fields

T0 review · 4 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that both spacetime non-commutativity θ and Einstein-tensor coupling η suppress the absorption cross-section of scalar waves by making the effective potential barrier thicker and more reflective, and that the grey-body/quas

desk verdict A plausible new computation whose central curves have an unspecified computational origin: the paper says WKB is unsuitable for the background, but never states whether the headline cross-sections come from WKB or from an undescribed direct integration. read the letter →

arxiv 2511.16012 v2 pith:4J3ELI4J submitted 2025-11-20 gr-qc

Sihao Fan , Wenjun Guo , Chen Wu This is my paper · ORCID
classification gr-qc
keywords non-commutativeblackholegrey-bodyfactorabsorptioncross-sectionEinstein-tensorcouplingscalarfieldperturbationquasinormalmodesWKBapproximationeffectivepotential
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

This paper studies a massive scalar field non-minimally coupled to the Einstein tensor around a non-commutative black hole. It claims that both the non-commutativity parameter θ and the coupling constant η make the effective potential barrier wider and more reflective, so the grey-body factor transitions more gradually from zero to unity and the total absorption cross-section is suppressed. It also tests a recently proposed correspondence that reconstructs grey-body factors from quasinormal-mode frequencies, and finds it accurate for large angular momentum l but not for small l. The physical upshot is that quantum spacetime fuzziness and derivative coupling to gravity act alike on black-hole scattering.

What carries the argument

The argument hinges on the effective potential V_eff(r) in the radial wave equation obtained after separating the scalar field into partial waves. V_eff is built from the non-commutative metric function f(r)=1-(4M/(r√π))γ(3/2,r²/(4θ)), the Einstein-tensor components encoded in A(r) and B(r), and the coupling η; it reduces to the Schwarzschild potential when θ→0 or η→0. The grey-body factor Γ_ωl is the transmission probability through this barrier, computed either by the WKB formula Γ=(1+e^{2πiK})^{-1} or by partial-wave numerical integration, and the absorption cross-section is the sum σ_abs=(π/ω²)Σ_l(2l+1)Γ_ωl. The same potential supplies the quasinormal frequencies via the WKB quantization

What would settle it

Compute the absorption cross-section by direct numerical integration of the radial wave equation with purely ingoing boundary condition at the event horizon and outgoing at infinity, for a fixed scalar mass m and a set of l values; then check whether increasing θ at fixed η (and η at fixed θ) always decreases σ_abs(ω) across the allowed range 0<θ<0.275811. If any frequency shows a larger cross-section for larger θ or η, the paper's central claim fails. For the correspondence, compute quasinormal frequencies by an independent method (time-domain evolution or matrix discretization) and compare t

Watch

Extended reading notes

Core claim

The paper's central claim is that for a massive scalar field non-minimally coupled to the Einstein tensor in the spacetime of a non-commutative black hole, the parameters θ (the non-commutativity scale) and η (the coupling constant) act on the effective potential in the same direction: larger values deepen and widen the negative region of the potential barrier. As a result, the grey-body factor Γ_ωl(ω) turns from zero to unity more gradually, and the partial and total absorption cross-sections σ_abs(ω) are suppressed. The paper also asserts that the recently proposed correspondence that reconstructs the grey-body factor from the fundamental quasinormal mode and first overtone is accurate in

Load-bearing premise

The paper relies on the numerical curves of grey-body factors and absorption cross-sections being produced by a reliable method, but it never states which method produced the final figures; it even reports that the WKB method is not suitable for non-commutative black holes, so if the curves came from WKB, the central claim rests on an invalidated tool, and if they came from direct integration, the integration scheme and boundary conditions are unspecified.

Editorial extensions

If this is right

  • Larger θ or η suppresses the total absorption cross-section, so non-commutative black holes with stronger Einstein-tensor coupling absorb less scalar radiation at fixed mass.
  • The grey-body factor curves flatten and shift to lower frequencies as either parameter grows, meaning the black hole's emission spectrum via Hawking radiation is modified at low frequencies.
  • The grey-body/quasinormal correspondence is a reliable shortcut for large l but not for small l in these backgrounds, so calculations should use direct integration for low multipoles.
  • The similar effect of θ and η suggests that observations of black-hole scattering alone cannot easily distinguish spacetime non-commutativity from derivative coupling.

Reading between the lines

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

  • One could compute the Hawking radiation power spectrum using these grey-body factors; the suppression implies a dimmer and softer black hole spectrum for fixed mass, with the effect growing as θ and η increase.
  • A natural numerical follow-up is to compute the same cross-sections with a fully specified direct integration (boundary conditions, scalar mass m, partial-wave cutoff) and compare against the WKB-based curves; the paper does not state which method produced its final figures.
  • The approximate degeneracy between θ and η could be tested by searching for pairs (θ1,η1) and (θ2,η2) that yield nearly identical grey-body factors; if it holds, it would allow a two-parameter family of effective potentials with identical scattering, potentially hiding quantum-gravity corrections.
  • The correspondence's accuracy could be extended to include higher overtones and to test the next-to-eikonal corrections explicitly against numerical quasinormal-mode data for low l.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies a massive scalar field non-minimally coupled to the Einstein tensor in a non-commutative Schwarzschild-inspired black-hole background. It claims to compute grey-body factors and absorption cross-sections via the partial-wave method, and to test the Konoplya-Zhidenko correspondence between grey-body factors and quasinormal-mode frequencies. The central physical claim is that increasing either the non-commutativity parameter θ or the Einstein-tensor coupling η suppresses the scalar absorption cross-section, and that the grey-body/QNM correspondence becomes accurate in the large-angular-momentum limit l→∞. The effective potential Veff is presented in Eq. (11), and grey-body factors are plotted for various θ and η; total and partial absorption cross-sections are plotted in Fig. 4.

Significance. If the central numerical claims are correct, the paper provides a concrete example of how quantum-gravity-inspired spacetime fuzziness (θ) and non-minimal derivative coupling (η) affect black-hole scattering in the same qualitative direction, and it extends tests of the Konoplya-Zhidenko correspondence beyond Schwarzschild. The η=0 limit of Eq. (11) correctly reduces to the standard massive-scalar effective potential f[l(l+1)/r² + m²] + ff'/r, which is a useful internal consistency check. However, the manuscript does not provide the full derivation of Veff, does not specify the numerical method behind the headline cross-section curves, and does not give the numerical details needed for independent verification. These omissions are load-bearing because the paper itself states that WKB is not suitable for non-commutative black holes, yet the method section initially says WKB is employed. No reproducible code or data tables are included.

major comments (4)
  1. [§I, §III, Figs. 3–4] The manuscript is internally ambiguous about which method generated the central grey-body and absorption cross-section curves. §I states 'we employ the sixth-order WKB approximation method to enhance the precision of our calculations', while §III, after comparing WKB with direct numerical integration, states 'the WKB method is not suitable for non-commutative black holes'. Figures 3 and 4, which support the abstract's claim that larger θ and η suppress absorption, are not labeled with the method used. If they come from sixth-order WKB, the central claim is computed with a method the paper itself invalidates for this background; if they come from direct numerical integration, the integration scheme, boundary conditions, scalar mass m, and partial-wave truncation in Eq. (26) are all unstated. This is load-bearing for the abstract's central claim and must be clarified or the numerical secti
  2. [§II, Eq. (11)] The derivation from the Lagrangian Eq. (2) to the effective potential Eq. (11) is only described as 'expanding and rearranging', with no intermediate steps. Since every subsequent result — quasinormal modes, grey-body factors, absorption cross-sections, and the correspondence test — depends on Veff, this is a central derivation, not a presentation detail. The authors should provide the full reduction, including the treatment of the ηGμν terms, the definition of b(r) in Eq. (9), and the relation between A(r), B(r), and the Ricci scalar. The η=0 limit check is reassuring but not a substitute.
  3. [§III, Eqs. (19)–(24), Fig. 2] The correspondence test relies on the quasinormal frequencies ω0 and ω1. These appear to be taken from the authors' earlier work Ref. [28], which uses the same effective potential (not derived in the present paper) and, according to the present manuscript, WKB methods that are 'not suitable for non-commutative black holes'. The accuracy of the KZ correspondence is then judged by comparing Eq. (19) with 'direct numerical integration', but the direct numerical recipe is not given. Without stating how ω0, ω1, and the direct-integration grey-body factors were computed, the claim that the correspondence is accurate for large l cannot be independently assessed.
  4. [§IV, Eq. (26), Fig. 4] The absorption cross-section results depend on an infinite partial-wave sum. The manuscript does not state the scalar-field mass m (included in Eq. (2) and Veff), the number of partial waves retained, or the high-frequency truncation criterion. Given that Fig. 4 claims oscillations around the geometric-optics limit, the truncation matters. The paper also does not give numerical values or error estimates for the plotted curves, so the monotonic ordering with θ and η cannot be verified quantitatively.
minor comments (4)
  1. [Abstract, Title] The abstract refers to 'non-exchange parameter θ' and the title contains a line break 'Non-Com mutative'. These should be corrected. Also, 'polarization method' in the abstract and 'partial wave method' in the text should be made consistent.
  2. [Eq. (14)] The variable χ is used in the asymptotic solutions and Hankel-function expansions but never defined. It should be the tortoise coordinate r*; please define it explicitly and state the boundary conditions in terms of r*.
  3. [Figs. 3–4] The figure labels are difficult to read in the extracted text and the parameter values (e.g., exact θ and η for each curve, and the value of m) are not stated in the captions. Since the paper claims parametric trends, the figures should be reproducible from the captions.
  4. [§III, Eq. (20)] The WKB equation is written with trailing '...' and the sign/truncation of the higher-order terms is unclear. For reproducibility, the precise order at which the calculation was truncated should be stated, especially because the paper says sixth-order WKB is employed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the absorption cross-sections are computed from the effective potential and grey-body factors, not from the quantities being 'predicted'.

full rationale

The central claim that larger θ and η suppress the absorption cross-section is a direct numerical consequence of the paper's own computational chain. The effective potential V_eff (Eq. 11) is derived from the non-commutative metric (Eq. 12) and the scalar field Lagrangian with Einstein-tensor coupling (Eq. 2). The grey-body factor is defined as Γ_l(ω)=1−|A_out/A_in|² (Eq. 18), and the absorption cross-section is the fixed partial-wave sum σ_abs(ω)=(π/ω²)Σ(2l+1)Γ_l(ω) (Eq. 26). Larger θ and η modify the potential barrier, and the reported suppression of σ_abs follows from solving for Γ_l; it is not fitted from or defined in terms of the cross-section. The KZ correspondence check is presented as a comparison of the WKB-based formula with direct numerical integration: 'we compare the grey-body factors obtained via the WKB approach with those from direct numerical integration' (Sec. III). This gives it independent grounding, even if the QNM frequencies ω0, ω1 may have been taken from the same group's earlier WKB computations. The self-citations [28] and [34] are used for the metric's computational form and for the parameter range, not as the load-bearing justification for the absorption result. A genuine reproducibility concern is present: the paper first says 'we employ the sixth-order WKB approximation method' (Sec. I) and later says 'the WKB method is not suitable for non-commutative black holes' (Sec. III), without specifying which method produced Figs. 3 and 4. But this is a methodological ambiguity and a correctness/reproducibility issue, not circularity. No step in the derivation reduces by construction to its own input.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities: the metric, the coupling, and the correspondence are all inherited from prior literature. The load-bearing free choices are the scanned parameters θ and η, the unstated mass m, and the self-cited QNM frequencies. The most fragile assumptions are the unshown reduction to the Schrödinger equation and the contradictory claims about WKB applicability.

free parameters (4)
  • θ (non-commutativity parameter) = scanned in figures; valid range 0 < θ < 0.275811 per refs. [32,34]
    Parameter of the NSS metric (Eq. 12), chosen by hand in the plots; the first headline result is its effect on the cross-section.
  • η (Einstein-tensor coupling constant) = scanned in figures; values not stated
    Coupling strength in the scalar Lagrangian (Eq. 2), chosen by hand; the second headline result is its effect.
  • m (scalar field mass) = not stated; presumably 0
    The Lagrangian (Eq. 2) is for a massive scalar but the text never gives m for the computation; the absorption formula Eq. (26) is the massless form.
  • QNM frequencies ω₀, ω₁ used in the correspondence test = from ref. [28] (same group)
    Inputs to the KZ correspondence (Eqs. 22-24); inherited from the authors' prior WKB computation rather than independently verified here.
assumptions (5)
  • domain assumption The NSS metric f(r) = 1 - (4M/(r√π))γ(3/2, r²/4θ) (Eq. 12) is the correct non-commutative black-hole background.
    Taken from ref. [32]; the paper does not derive it and the spacetime is not a vacuum Einstein solution.
  • domain assumption The Einstein-tensor-coupled scalar Lagrangian L_pert = -√(-g)/2[(g^μν + ηG^μν)∂_μΦ∂_νΦ + m²Φ²] (Eq. 2) is the correct matter sector.
    Motivated by refs. [30,31]; stability and unitarity of this coupling on this background are not established here.
  • ad hoc to paper The ansatz Ψ = e^{-iωt} b(r)/r R(r) Y_lm with b(r) = √(1-ηA(r))/r (Eqs. 4, 9) reduces the field equation exactly to the Schrödinger form Eq. (10) with V_eff Eq. (11).
    The reduction is asserted ('expanding and rearranging... yields') and not shown; the b(r) choice is stated without proof and inherited from ref. [28].
  • ad hoc to paper The sixth-order WKB approximation is accurate enough for the parameter ranges plotted.
    Section I asserts acceptable accuracy for small θ/η citing [28]; Section III states 'the WKB method is not suitable for non-commutative black holes' based on Fig. 2. The two claims are not reconciled.
  • domain assumption The Konoplya-Zhidenko correspondence formulas (Eqs. 19-24) are valid and their truncation is accurate at the l values used.
    External result from ref. [20]; the paper applies it rather than deriving it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Graybody factors and absorption cross-sections of non-exchange black holes in Instein-coupled scalar fields." pith.science (2026). https://pith.science/paper/4J3ELI4J

@misc{pith2026251116012,
  author       = {Pith},
  title        = {Pith review of: Graybody factors and absorption cross-sections of non-exchange black holes in Instein-coupled scalar fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4J3ELI4J}},
  note         = {Machine review of arXiv:2511.16012}
}
abstract

This paper studies scalar field perturbations coupled with Einstein tensors of non-exchange black holes. We use the polarization method to calculate graybody factors and absorption cross-sections selected by different parameters, and verify the latest correspondence between graybody factors and quasi-normal states. The results show that the larger the value of the non-exchange parameter $\theta$ and the coupling constant $\eta$ introduced into the model, the smaller the absorption cross-section. Furthermore, we found that this correspondence is accurate for non-commutative black holes at the $1$ limit of large angular momentum quantum numbers.

Figures

Figures reproduced from arXiv: 2511.16012 by the authors.

Figure 1
Figure 1. FIG. 1. Effective potential energy diagrams for different val [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The grey-body factors under different parameters. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Grey-body factors under different parameters. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Partial and total absorption cross-sections for diffe [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

39 extracted references · 1 linked inside Pith

  1. [28]

    Z. Yan, C. Wu, and W. Guo, Quasinormal modes of scalar field coupled to einstein’s tensor in the non-commutative geometry inspired black hole, Nuclear Physics B 973, 115595 (2021)

    2021

  2. [1]

    S. W. Hawking, Particle creation by black holes, Com- munications in Mathematical Physics 43, 199 (1975)

    1975

  3. [2]

    D. N. Page, Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Physical Review D 13, 198 (1976)

    1976

  4. [3]

    D. N. Page, Particle emission rates from a black hole. II. massless particles from a rotating hole, Physical Review D 14, 3260 (1976), part II

    1976

  5. [4]

    R. A. Konoplya and A. Zhidenko, Correspondence be- tween grey-body factors and quasinormal frequencies for rotating black holes, Physics Letters B 861, 139288 (2025)

    2025

  6. [5]

    Abdalla, B

    E. Abdalla, B. Cuadros-Melgar, R. D. B. Fontana, J. De Oliveira, E. Papantonopoulos, and A. B. Pavan, Instability of a reissner-nordstr¨ om-ads black hole under perturbations of a scalar field coupled to the einstein ten- 7 /s48/s46/s52 /s48/s46/s54 /s48/s46/s56 /s49/s46/s48 /s49/s46/s50 /s49/s46/s52 /s49/s46/s54 /s49/s46/s56 /s50/s46/s48 /s48 /s53/s48 /s4...

    2019

  7. [6]

    H. S. Vieira and V. B. Bezerra, Confluent heun func- tions and the physics of black holes: Resonant frequen- cies, hawking radiation and scattering of scalar waves, Annals of Physics 373, 28 (2016)

    2016

  8. [7]

    Abdujabbarov, F

    A. Abdujabbarov, F. Atamurotov, N. Dadhich, B. Ahme- dov, and Z. Stuchl ´ ık, Energetics and optical properties of 6-dimensional rotating black hole in pure gauss-bonnet gravity, The European Physical Journal C 75, 399 (2015)

    2015

Show all 39 references
  1. [8]

    L. C. S. Leite, L. C. B. Crispino, E. S. De Oliveira, C. F. B. Macedo, and S. R. Dolan, Absorption of massless scalar field by rotating black holes, International Journal of Modern Physics D 25, 1641024 (2016)

    2016

  2. [9]

    L. C. S. Leite, C. L. Benone, and L. C. B. Crispino, Scalar absorption by charged rotating black holes, Physical Review D 96, 044043 (2017)

    2017

  3. [10]

    A. H. Chamseddine, Deforming einstein’s gravity, Physics Letters B 504, 33 (2001)

    2001

  4. [11]

    Aschieri, M

    P. Aschieri, M. Dimitrijevi´ c, F. Meyer, and J. Wess, Non- commutative geometry and gravity, Classical and Quan- tum Gravity 23, 1883 (2006)

    2006

  5. [12]

    Kobakhidze, Theta-twisted gravity, International Journal of Modern Physics A 23, 2541 (2008)

    A. Kobakhidze, Theta-twisted gravity, International Journal of Modern Physics A 23, 2541 (2008)

    2008

  6. [13]

    Smailagic and E

    A. Smailagic and E. Spallucci, Lorentz invariance, uni - tarity and uv-finiteness of qft on noncommutative space- time, Journal of Physics A: Mathematical and General 37, 7169 (2004)

    2004

  7. [14]

    Nicolini, Noncommutative black holes, the final appe al to quantum gravity: A review, International Journal of Modern Physics A 24, 1229 (2009)

    P. Nicolini, Noncommutative black holes, the final appe al to quantum gravity: A review, International Journal of Modern Physics A 24, 1229 (2009)

    2009

  8. [15]

    Gruppuso, Newton’s law in an effective non- commutative space–time, Journal of Physics A: Math- ematical and General 38, 2039 (2005)

    A. Gruppuso, Newton’s law in an effective non- commutative space–time, Journal of Physics A: Math- ematical and General 38, 2039 (2005)

  9. [16]

    Nicolini, A model of radiating black hole in noncom- mutative geometry, Journal of Physics A: Mathematical and General 38, L631 (2005)

    P. Nicolini, A model of radiating black hole in noncom- mutative geometry, Journal of Physics A: Mathematical and General 38, L631 (2005)

    2005

  10. [17]

    Okabayashi and N

    K. Okabayashi and N. Oshita, Greybody factors im- printed on black hole ringdowns. ii. merging binary black holes, Physical Review D 110, 064086 (2024)

    2024

  11. [18]

    Oshita, Greybody factors imprinted on black hole ringdowns: An alternative to superposed quasi-normal modes, arXiv preprint arXiv:2309.05725 (2023)

    N. Oshita, Greybody factors imprinted on black hole ringdowns: An alternative to superposed quasi-normal modes, arXiv preprint arXiv:2309.05725 (2023)

    2023 arXiv

  12. [19]

    Oshita, Thermal ringdown of a kerr black hole: Over- tone excitation, fermi-dirac statistics and greybody fac- tor, Journal of Cosmology and Astroparticle Physics 2023 (04), 013

    N. Oshita, Thermal ringdown of a kerr black hole: Over- tone excitation, fermi-dirac statistics and greybody fac- tor, Journal of Cosmology and Astroparticle Physics 2023 (04), 013

    2023

  13. [20]

    R. A. Konoplya and A. Zhidenko, Correspondence be- tween grey-body factors and quasinormal modes, Journal of Cosmology and Astroparticle Physics 2024 (09), 068

    2024

  14. [21]

    S. V. Bolokhov and M. Skvortsova, Correspondence be- tween quasinormal modes and grey-body factors of spher- ically symmetric traversable wormholes, Journal of Cos- mology and Astroparticle Physics 2025 (04), 025

    2025

  15. [22]

    K. Aoki, M. A. Gorji, and S. Mukohyama, A consistent theory of d → 4 einstein-gauss-bonnet gravity, Physics Letters B 810, 135843 (2020)

    2020

  16. [23]

    R. A. Konoplya and Z. Stuchl ´ ık, Are eikonal quasinor- mal modes linked to the unstable circular null geodesics?, Physics Letters B 771, 597 (2017)

    2017

  17. [24]

    Iyer and C

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

    1987

  18. [25]

    R. A. Konoplya, Quasinormal behavior of the d- 8 dimensional schwarzschild black hole and the higher or- der wkb approach, Physical Review D 68, 024018 (2003)

    2003

  19. [26]

    B. F. Schutz and C. M. Will, Black hole normal modes—a semianalytic approach, The Astrophysical Journal 291, L33 (1985)

    1985

  20. [27]

    K. Das, S. Pramanik, and S. Ghosh, Quasi- normal mode spectra for odd parity perturba- tions in spacetimes with smeared matter sources, Physical Review D 99, 024039 (2019)

    2019

  21. [29]

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

    2019

  22. [30]

    Amendola, Cosmology with nonminimal derivative couplings, Physics Letters B 301, 175 (1993)

    L. Amendola, Cosmology with nonminimal derivative couplings, Physics Letters B 301, 175 (1993)

    1993

  23. [31]

    S. V. Sushkov, Exact cosmological solutions with non- minimal derivative coupling, Physical Review D 80, 103505 (2009)

    2009

  24. [32]

    Nicolini, A

    P. Nicolini, A. Smailagic, and E. Spallucci, Noncommut a- tive geometry inspired schwarzschild black hole, Physics Letters B 632, 547 (2006)

    2006

  25. [33]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun, Handbook of Mathe- matical Functions (Dover, 1964)

    1964

  26. [34]

    Z. Yan, C. Wu, and W. Guo, Scalar field quasi- normal modes of noncommutative high dimensional schwarzschild-tangherlini black hole spacetime with smeared matter sources, Nuclear Physics B 961, 115217 (2020)

    2020

  27. [35]

    Matyjasek and M

    J. Matyjasek and M. Opala, Quasinormal modes of black holes: The improved semianalytic approach, Physical Re- view D 96, 024011 (2017)

    2017

  28. [36]

    D´ ecanini, A

    Y. D´ ecanini, A. Folacci, and B. Raffaelli, Unstable cir - cular null geodesics of static spherically symmetric black holes, regge poles, and quasinormal frequencies, Physical Review D 81, 104039 (2010)

    2010

  29. [37]

    D´ ecanini, A

    Y. D´ ecanini, A. Folacci, and B. Raffaelli, Fine structu re of high-energy absorption cross sections for black holes, Classical and Quantum Gravity 28, 175021 (2011)

    2011

  30. [38]

    Padmanabhan, Cosmological constant—the weight of the vacuum, Physics Reports 380, 235 (2003)

    T. Padmanabhan, Cosmological constant—the weight of the vacuum, Physics Reports 380, 235 (2003)

    2003

  31. [39]

    Sanchez, Absorption and emission spectra of a schwarzschild black hole, Physical Review D 18, 1030 (1978)

    N. Sanchez, Absorption and emission spectra of a schwarzschild black hole, Physical Review D 18, 1030 (1978)

    1978

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.