Pith. sign in

REVIEW 2 major objections 4 minor 78 references

This paper establishes that, for a Husain generalized Vaidya black hole, the barotropic equation-of-state parameter α fixes the sign of the extra matter term once the weak energy condition holds, and that this sign determines whether the ph

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 17:50 UTC pith:B3RBF2HJ

load-bearing objection A competent extension of Vaidya shadow theory to the Husain spacetime, with exact benchmarks that support the branch pattern, but the α>1/2 branch violates the paper's own null-radiation WEC near the origin and the abstract overstates the perturbative caveat. the 2 major comments →

arxiv 2607.17483 v1 pith:B3RBF2HJ submitted 2026-07-20 gr-qc

Shadow of the generalized Vaidya black hole

Vitalii Vertogradov , Ali \"Ovg\"un This is my paper
classification gr-qc PACS 95.30.Sf04.70.-s97.60.Lf04.50.Kd
keywords black hole shadowgeneralized Vaidya spacetimeHusain solutionbarotropic equation of statephoton spherehomothetic Killing vectorquasistatic black holeweak energy condition
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper works with the Husain solution, a generalized Vaidya black hole whose extra matter obeys a barotropic equation of state P = αρ. It shows that within the branches allowed by the weak energy condition, the value of α determines the optical effect: for 0 ≤ α < 1/2 the photon sphere and shadow are enlarged relative to the self-similar Vaidya geometry, while for 1/2 < α ≤ 1 they are reduced. For the genuinely time-dependent geometry it derives a quasistatic evolution equation and a local criterion: the shadow grows or shrinks according to the effective null influx at the photon surface, not according to the separate signs of the mass and charge rates. A sympathetic reader would care because this gives analytical control over shadows in dynamical, matter-dressed black holes, and it identifies the high-pressure branch as the one naturally producing shadows smaller than the uncharged Vaidya reference.

Core claim

The central claim is that the barotropic parameter α in the Husain spacetime acts as a switch: once the weak energy condition is imposed, it fixes the sign of the extra term, and that sign alone decides whether the photon sphere and shadow radius move outward or inward relative to the self-similar Vaidya background. The paper proves this by mapping the self-similar geometry to a conformally static metric, computing the homothetic photon surface, and treating the Husain term as a deformation; the exact α = 0 and α = 1 solutions confirm the general branch result. In the time-dependent case the paper shows that the instantaneous critical impact parameter evolves according to d ln b_ph/dv = -(1/

What carries the argument

The machinery combines a homothetic Killing vector, a scaling symmetry that lets the time-dependent Vaidya-type metric be rewritten, up to a conformal factor, as a static metric, with a perturbative deformation method: the Husain matter term is written as an exponential factor g(R) multiplying the Vaidya lapse function, so the signs of g and g' at the Vaidya photon sphere give the first-order shifts of the impact parameter and photon-sphere radius. For the dynamical case, the same photon-surface condition is differentiated along v to give a drift equation for r_ph and a local growth criterion for the impact parameter.

Load-bearing premise

The branch classification assumes the Husain term is a small deformation of the Vaidya geometry (Eq. 101) and that the weak energy condition indeed holds for the self-similar branches; outside that perturbative regime, or if the energy condition fails in the photon region, the stated signs do not follow.

What would settle it

For a concrete intermediate α (say α = 0.3 or 0.7) with moderate ν, solve the exact photon-sphere condition numerically and compare the shadow radius to the first-order prediction; if the shift changes sign or is not first-order small, the perturbative branch criterion fails. Alternatively, compute μ^(n) for the α > 1/2 self-similar branch at small r — if it turns negative, that branch violates the null energy condition and is excluded from the physical domain.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • For 0 ≤ α < 1/2, the Husain matter sector enlarges both the photon-sphere radius and the shadow relative to self-similar Vaidya; for 1/2 < α ≤ 1 it decreases both.
  • The exact α = 0 and α = 1 cases validate the branch structure without relying on the first-order expansion.
  • In the quasistatic regime, shadow growth is set by the local influx criterion 2 Ṁ r_ph^{2α-1} + Ṅ > 0, not by the signs of Ṁ and Ṅ separately.
  • For the charge-like branch N = -Q², accretion can shrink the shadow when Q Ȯ/r_ph^{2α-1} exceeds Ṁ, while neutralization tends to enlarge it.
  • The high-pressure branch (α > 1/2) offers a concrete route to shadows smaller than the corresponding Vaidya or Schwarzschild reference, which is the direction favored by EHT observations of M87* and Sgr A*.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: The local influx criterion suggests a numerically testable prediction — ray-tracing on the fully dynamical Husain metric should reproduce the sign of d b_ph/dv from Eq. (162) when the evolution is slow, but may show deviations once the quasistatic approximation breaks.
  • Editorial extension: The paper's branch structure implies that a measurement of shadow size alone, combined with a mass estimate, could in principle discriminate between low-pressure and high-pressure matter sectors if the Vaidya baseline is known.
  • Editorial extension: The energy-condition radius r_nec introduced in Sec. V could be used as a diagnostic in simulations: if r_nec crosses the photon sphere during accretion, the shadow's growth direction should reverse, an effect that could be searched for in numerical collapse or accretion models.
  • Editorial extension: The paper leaves open whether the weak energy condition for the null radiation sector, μ^(n) ≥ 0, actually holds throughout the self-similar α > 1/2 branch; verifying this would determine whether that branch is physically admissible.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The manuscript studies null geodesics and shadows in the generalized Vaidya/Husain spacetime. After imposing a barotropic equation of state P=αρ, the authors isolate the self-similar subclass with M=μv and N=νv^{2α}, transform to conformally static coordinates via v=r0 e^{t/r0}, r=R e^{t/r0}, and derive the photon-surface condition f'(R)R-2f(R)=0 and critical impact parameter b²=R²/f. Around the Vaidya reference (ν=0), the sign of the deformation g(R_v) is used to argue that the WEC branch 0≤α<1/2 enlarges the photon sphere and shadow, while 1/2<α≤1 shrinks them; exact solutions for α=0 and α=1 are provided as benchmarks. In the time-dependent case the authors derive quasistatic drift equations for r_ph(v) and b_ph(v), concluding that the shadow evolution is controlled by the local effective influx 2Mdot r^{2α-1}+Ndot in the photon region rather than by the separate signs of Mdot and Ndot.

Significance. If correct, the result provides a clean analytical extension of dynamical shadow theory beyond pure Vaidya radiation and a concrete way to connect the equation-of-state parameter α to observable shadow size. The conformal transformation and null-geodesic reduction are standard and the exact α=0 and α=1 examples are valuable checks. The quasistatic criterion of Sec. V is a useful local diagnostic. However, the central branch classification rests on an energy-condition premise that is not verified for α>1/2, and the general-α statement is proven only in the perturbative regime of Eq. (101). These issues do not invalidate the framework but require qualification and repair before the abstract claim is fully supported.

major comments (2)
  1. [Sec. II, Eq. (13); Sec. IV, Eq. (150)] The paper's stated null/weak energy condition for the type-II sector is μ^(n)≥0 (Eq. (13)). For the self-similar Husain branch (24)-(25), Eq. (150) gives μ^(n)=2[μ+αν v^{2α-1}r^{1-2α}]/r². On the branch 1/2<α≤1, type-I WEC forces ν<0 (Eq. (22)), so αν<0. Since 1-2α<0, the second term diverges to -∞ as r→0, and μ^(n)<0 in an open inner region r<v(|αν|/μ)^{1/(2α-1)}. Thus the 'weak-energy-condition branch' α>1/2 violates the paper's own Eq. (13) unless additional parameter restrictions are imposed; the paper only enforces ρ≥0 and ρ+P≥0. This is load-bearing because the abstract's qualifier 'within the weak-energy-condition branches' is exactly what selects the α>1/2 shrinking branch. Please either impose μ^(n)≥0 at the photon sphere and show that it holds in the relevant parameter regime, or restrict/amend the claim.
  2. [Abstract and Sec. IV, Eq. (101)] The branch classification for general α is obtained to first order in the deformation, with smallness condition (101); the conclusion in Sec. VI correctly says 'within the perturbative regime'. The abstract, however, presents the α dependence as a definitive feature of the WEC branches without this caveat. Since intermediate values of α are not solved exactly, the statement 'the branch 0≤α<1/2 increases ... whereas 1/2<α≤1 decreases' is currently established only for sufficiently small |ν| (plus the exact endpoints α=0,1). Please add the perturbative qualifier in the abstract and in the statement of the main result.
minor comments (4)
  1. [Sec. III, around Eq. (79)] The text refers to 'Eq. (79)' before displaying the equation; renumber or rephrase to avoid self-reference.
  2. [Eqs. (6) and (24)-(25)] The same symbol μ is used for the mass parameter in M(v)=μv and for the null-radiation density in Eq. (6). This is acknowledged in the text but remains a source of confusion; consider using a distinct symbol for one of them.
  3. [Sec. II, Eqs. (35)-(36)] The notation ν(α) is introduced, but the text then treats ν as a positive amplitude with the sign carried by the α-dependent branch. Please make this convention explicit and consistently applied.
  4. [Sec. V, Eq. (166)] The energy-condition radius r_nec(v) assumes ̇M(v)≠0 and 2α-1≠0. The special cases ̇M=0 and α=1/2 are not discussed; a brief comment would prevent confusion.

Circularity Check

0 steps flagged

No significant circularity: the shadow-shift and quasistatic-evolution claims follow by direct algebra from the metric and photon-surface conditions, with exact α=0 and α=1 benchmarks providing independent confirmation.

full rationale

The derivation chain is self-contained. Starting from the Husain mass function (19) and the conformally static form (30), the paper defines the null effective potential (42) and obtains the homothetic photon surface from f'(R)R-2f(R)=0 and b^2=R^2/f(R) (Eq. 45). The branch classification for α is a first-order consequence of writing f=f_V e^g (Eq. 50) and using δln b_ph = -1/2 g(R_v)+O(ν²) (Eq. 102), which follows directly from b^2=R^2/f; no fitted parameter is involved. The two exact cases α=0 (Eqs. 116-123) and α=1 (Eqs. 135-143) independently confirm the same enlargement/reduction pattern, so the dependence on the authors' perturbative method [72] is a methodological citation, not a circular reduction. The quasistatic criterion (158)-(163) is obtained by differentiating the defining relation b^2=r^2/f with the photon-surface condition, so it is a direct consequence of the definitions, not an input renamed as a prediction. Two non-circular caveats should be noted for correctness rather than circularity: (i) the null-radiation WEC μ^(n)≥0 (Eq. 13) is never checked for the self-similar branches; for α>1/2 with ν<0, Eq. (150) gives μ^(n)=2[μ+αν v^{2α-1} r^{1-2α}]/r^2, which becomes negative near r→0, so the 'weak-energy-condition branch' qualifier is not fully established; (ii) the abstract omits the small-deformation condition (Eq. 101) that limits the perturbative branch statement. Neither issue makes any derived result equivalent to its input by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

No new physical entities are introduced; the matter sector is the standard Husain/barotropic type-I fluid plus null radiation, and the charge-like parameter N is inherited from the Husain solution (Ref. [55]). The free parameters r0, μ, ν, and α are model inputs rather than fit parameters.

free parameters (4)
  • r0
    Arbitrary length scale introduced in the conformal coordinate transformation (Eqs. 27-28, 56-57); cancels from physical shadow observables.
  • mu (mass parameter)
    Sets the Vaidya reference in M(v)=μv (Eq. 25); model input, not fitted.
  • nu (Husain amplitude)
    Amplitude of the additional matter term in N(v)=νv^{2α} (Eq. 24); sign fixed by WEC (Eqs. 35-36); perturbative parameter in Eq. (101).
  • alpha
    Barotropic equation-of-state parameter P=αρ (Eq. 16); ranges over [0,1] excluding 1/2 (Eq. 18); the branch label of the central claim.
axioms (5)
  • standard math Null geodesics are invariant under conformal transformations up to reparametrization
    Used in Secs. III-IV to analyze the conformally static metric instead of the original Husain metric.
  • domain assumption Homothetic self-similar ansatz M(v)=μv, N(v)=νv^{2α}
    Restricts the Husain solution to the class admitting a homothetic Killing vector (Eqs. 24-25); not the most general Husain solution.
  • domain assumption Weak/dominant energy conditions for the type-I sector: ρ≥0, ρ+P≥0 (and |α|≤1)
    Fixes the sign of N(v) (Eqs. 20-22, 35-36); the central branch classification depends on these signs.
  • domain assumption Perturbative method of Ref. [72]: sign of g(R) and g'(R) at the reference photon sphere determines first-order shift of shadow and photon-sphere radii
    Imported from the authors' earlier paper; used in Sec. IV to derive δln b and δRph (Eqs. 102, 106).
  • domain assumption Quasistatic slow-evolution approximation: M(v) and N(v) vary on timescales much longer than the photon orbital timescale
    Underpins the instantaneous photon-surface and impact-parameter equations in Sec. V (before Eq. 151).

pith-pipeline@v1.3.0-alltime-deepseek · 18443 in / 22999 out tokens · 186136 ms · 2026-08-01T17:50:26.721507+00:00 · methodology

0 comments
read the original abstract

In this paper, we investigate the shadow of the generalized Vaidya black hole described by the Husain solution. Assuming a barotropic equation of state for the additional matter sector, we first identify the self-similar class admitting a homothetic Killing vector and transform the geometry to a conformally static form. This allows us to derive the effective potential for null geodesics in the conformally static representative, determine the corresponding homothetic photon surface, and then transform the result back to the original generalized Vaidya coordinates. We show that, within the weak-energy-condition branches, the parameter $\alpha$ controlling the equation of state determines whether the shadow is enlarged or reduced relative to the Vaidya case: the branch $0\leq\alpha<1/2$ increases the photon-sphere and shadow radii, whereas the branch $1/2<\alpha\leq 1$ decreases them. We then turn to the genuinely time-dependent Husain metric and derive quasistatic slow-evolution equations for the instantaneous photon surface and critical impact parameter. In particular, we show that the growth or contraction of the shadow is governed by the local effective influx in the photon region rather than by the signs of $\dot M$ and $\dot N$ separately. For the charge-like branch, this yields a transparent criterion for when accretion enlarges the shadow and when rapid charge growth instead causes it to shrink.

Figures

Figures reproduced from arXiv: 2607.17483 by Ali \"Ovg\"un, Vitalii Vertogradov.

Figure 1
Figure 1. Figure 1: FIG. 1. Dimensionless photon-sphere radius [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

78 extracted references · 65 linked inside Pith

  1. [1]

    Writing f(R) =f V (R)eg(R),(104) where fV (R)is the self-similar Vaidya lapse function, one has F(R) =F V (R) +g ′(R).(105) Expanding around the Vaidya photon sphere Rv, defined by FV (Rv) = 0, gives δRph =− g′(Rv) F ′ V (Rv) .(106) Since F ′ V (Rv) < 0in the physical parameter range, the sign of the photon-sphere shift is the same as the sign of g′(Rv). ...

  2. [2]

    Opti- cal reference geometry for stationary and static dynamics

    M. A. Abramowicz, B. Carter, and J. P. Lasota, “Opti- cal reference geometry for stationary and static dynamics.” General Relativity and Gravitation20, 1173–1183 (1988)

    1988

  3. [3]

    The Geometry of photon surfaces,

    Clarissa-Marie Claudel, K. S. Virbhadra, and G. F. R. Ellis, “The Geometry of photon surfaces,” J. Math. Phys.42, 818–838 (2001), arXiv:gr-qc/0005050. 13

    Pith/arXiv arXiv 2001

  4. [4]

    Shadows and strong gravitational lensing: a brief review,

    Pedro V. P. Cunha and Carlos A. R. Herdeiro, “Shadows and strong gravitational lensing: a brief review,” Gen. Rel. Grav.50, 42 (2018), arXiv:1801.00860 [gr-qc]

    Pith/arXiv arXiv 2018

  5. [5]

    Calculating black hole shadows: Review of analytical studies,

    Volker Perlick and Oleg Yu. Tsupko, “Calculating black hole shadows: Review of analytical studies,” Phys. Rept.947, 1–39 (2022), arXiv:2105.07101 [gr-qc]

    Pith/arXiv arXiv 2022

  6. [6]

    Black Hole Shadows, Photon Rings, and Lensing Rings,

    Samuel E. Gralla, Daniel E. Holz, and Robert M. Wald, “Black Hole Shadows, Photon Rings, and Lensing Rings,” Phys. Rev. D100, 024018 (2019), arXiv:1906.00873 [astro- ph.HE]

    Pith/arXiv arXiv 2019

  7. [7]

    Shadow of rotating non-Kerr black hole,

    Farruh Atamurotov, Ahmadjon Abdujabbarov, and Bobo- murat Ahmedov, “Shadow of rotating non-Kerr black hole,” Phys. Rev. D88, 064004 (2013)

    2013

  8. [8]

    A coordinate-independent characterization of a black hole shadow,

    A. A. Abdujabbarov, L. Rezzolla, and B. J. Ahmedov, “A coordinate-independent characterization of a black hole shadow,” Mon. Not. Roy. Astron. Soc.454, 2423–2435 (2015), arXiv:1503.09054 [gr-qc]

    Pith/arXiv arXiv 2015

  9. [9]

    New method for shadow calculations: Application to parametrized axisymmetric black holes,

    Ziri Younsi, Alexander Zhidenko, Luciano Rezzolla, Roman Konoplya, and Yosuke Mizuno, “New method for shadow calculations: Application to parametrized axisymmetric black holes,” Phys. Rev. D94, 084025 (2016), arXiv:1607.05767 [gr-qc]

    Pith/arXiv arXiv 2016

  10. [10]

    Shadow of rotating regular black holes,

    Ahmadjon Abdujabbarov, Muhammed Amir, Bobomurat Ahmedov, and Sushant G. Ghosh, “Shadow of rotating regular black holes,” Phys. Rev. D93, 104004 (2016), arXiv:1604.03809 [gr-qc]

    Pith/arXiv arXiv 2016

  11. [11]

    Shadow of rotating worm- hole in plasma environment,

    Ahmadjon Abdujabbarov, Bakhtinur Juraev, Bobomurat Ahmedov, and Zdenˇ ek Stuchl ´ ık, “Shadow of rotating worm- hole in plasma environment,” Astrophys. Space Sci.361, 226 (2016)

    2016

  12. [12]

    Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole,

    Mingzhi Wang, Songbai Chen, and Jiliang Jing, “Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole,” JCAP10, 051 (2017), arXiv:1707.09451 [gr-qc]

    Pith/arXiv arXiv 2017

  13. [13]

    Black hole shadow in an asymptotically- flat, stationary, and axisymmetric spacetime: The Kerr- Newman and rotating regular black holes,

    Naoki Tsukamoto, “Black hole shadow in an asymptotically- flat, stationary, and axisymmetric spacetime: The Kerr- Newman and rotating regular black holes,” Phys. Rev. D 97, 064021 (2018), arXiv:1708.07427 [gr-qc]

    Pith/arXiv arXiv 2018

  14. [14]

    Shadow of a black hole surrounded by dark matter,

    R. A. Konoplya, “Shadow of a black hole surrounded by dark matter,” Phys. Lett. B795, 1–6 (2019), arXiv:1905.00064 [gr-qc]

    Pith/arXiv arXiv 2019

  15. [15]

    Quasinormal modes, stability and shadows of a black hole in the 4D Ein- stein–Gauss–Bonnet gravity,

    R. A. Konoplya and A. F. Zinhailo, “Quasinormal modes, stability and shadows of a black hole in the 4D Ein- stein–Gauss–Bonnet gravity,” Eur. Phys. J. C80, 1049 (2020), arXiv:2003.01188 [gr-qc]

    Pith/arXiv arXiv 2020

  16. [16]

    Rotating black holes in4 D Einstein-Gauss-Bonnet gravity and its shadow,

    Rahul Kumar and Sushant G. Ghosh, “Rotating black holes in4 D Einstein-Gauss-Bonnet gravity and its shadow,” JCAP 07, 053 (2020), arXiv:2003.08927 [gr-qc]

    Pith/arXiv arXiv 2020

  17. [17]

    Param- eter estimation of hairy Kerr black holes from its shadow and constraints from M87*,

    Misba Afrin, Rahul Kumar, and Sushant G. Ghosh, “Param- eter estimation of hairy Kerr black holes from its shadow and constraints from M87*,” Mon. Not. Roy. Astron. Soc. 504, 5927–5940 (2021), arXiv:2103.11417 [gr-qc]

    Pith/arXiv arXiv 2021

  18. [18]

    Effect of plasma on gravitational lensing by a Schwarzschild black hole immersed in perfect fluid dark matter,

    Farruh Atamurotov, Ahmadjon Abdujabbarov, and Wen- Biao Han, “Effect of plasma on gravitational lensing by a Schwarzschild black hole immersed in perfect fluid dark matter,” Phys. Rev. D104, 084015 (2021)

    2021

  19. [19]

    Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinor- mal modes and greybody factors,

    Mert Okyay and Ali ¨Ovg¨ un, “Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinor- mal modes and greybody factors,” JCAP01, 009 (2022), arXiv:2108.07766 [gr-qc]

    Pith/arXiv arXiv 2022

  20. [20]

    Testing dynamical torsion effects on the charged black hole’s shadow, deflection angle and greybody with M87* and Sgr. A* from EHT,

    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 Phys.448, 169197 (2023), arXiv:2206.02161 [gr-qc]

    Pith/arXiv arXiv 2023

  21. [21]

    Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes,

    Reggie C. Pantig, Leonardo Mastrototaro, Gaetano Lam- biase, and Ali ¨Ovg¨ un, “Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes,” Eur. Phys. J. C82, 1155 (2022), arXiv:2208.06664 [gr-qc]

    Pith/arXiv arXiv 2022

  22. [22]

    Testing symmergent gravity through the shadow image and weak field photon deflection by a rotating black hole using the M87∗ and Sgr. A∗ results,

    Reggie C. Pantig, Ali ¨Ovg¨ un, and Durmu¸ s Demir, “Testing symmergent gravity through the shadow image and weak field photon deflection by a rotating black hole using the M87∗ and Sgr. A∗ results,” Eur. Phys. J. C83, 250 (2023), arXiv:2208.02969 [gr-qc]

    Pith/arXiv arXiv 2023

  23. [23]

    Strong gravitational lens- ing and shadow constraint from M87* of slowly rotating Kerr-like black hole,

    Xiao-Mei Kuang and Ali ¨Ovg¨ un, “Strong gravitational lens- ing and shadow constraint from M87* of slowly rotating Kerr-like black hole,” Annals Phys.447, 169147 (2022), arXiv:2205.11003 [gr-qc]

    Pith/arXiv arXiv 2022

  24. [24]

    Constraining a modified gravity theory in strong gravitational lensing and black hole shadow observations,

    Xiao-Mei Kuang, Zi-Yu Tang, Bin Wang, and Anzhong Wang, “Constraining a modified gravity theory in strong gravitational lensing and black hole shadow observations,” Phys. Rev. D106, 064012 (2022), arXiv:2206.05878 [gr-qc]

    Pith/arXiv arXiv 2022

  25. [25]

    Photon regions, shadow observables, and constraints from M87* of a charged rotating black hole,

    Yuan Meng, Xiao-Mei Kuang, and Zi-Yu Tang, “Photon regions, shadow observables, and constraints from M87* of a charged rotating black hole,” Phys. Rev. D106, 064006 (2022), arXiv:2204.00897 [gr-qc]

    Pith/arXiv arXiv 2022

  26. [26]

    Constraints on charged symmergent black hole from shadow and lensing,

    Beyhan Puli¸ ce, Reggie C. Pantig, Ali ¨Ovg¨ un, and Durmu¸ s Demir, “Constraints on charged symmergent black hole from shadow and lensing,” Class. Quant. Grav.40, 195003 (2023), arXiv:2308.08415 [gr-qc]

    Pith/arXiv arXiv 2023

  27. [27]

    Shadow and greybody bounding of a regular scale-dependent black hole solution,

    Ali ¨Ovg¨ un, Reggie C. Pantig, and ´Angel Rinc´ on, “Shadow and greybody bounding of a regular scale-dependent black hole solution,” Annals Phys.463, 169625 (2024), arXiv:2402.14190 [gr-qc]

    Pith/arXiv arXiv 2024

  28. [28]

    Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data,

    Gaetano Lambiase, Reggie C. Pantig, and Ali ¨Ovg¨ un, “Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data,” EPL148, 49001 (2024), arXiv:2408.09620 [gr-qc]

    Pith/arXiv arXiv 2024

  29. [29]

    Traces of quantum gravitational correction at third-order curvature through the black hole shadow and particle deflec- tion at the weak field limit,

    Gaetano Lambiase, Reggie C. Pantig, and Ali ¨Ovg¨ un, “Traces of quantum gravitational correction at third-order curvature through the black hole shadow and particle deflec- tion at the weak field limit,” Phys. Dark Univ.46, 101597 (2024), arXiv:2406.18292 [gr-qc]

    Pith/arXiv arXiv 2024

  30. [30]

    Exploring the shadow of a rotating charged ModMax black hole,

    Khurshid Karshiboev, Farruh Atamurotov, Ahmadjon Abdu- jabbarov, Ali ¨Ovg¨ un, and Anvar Reyimberganov, “Exploring the shadow of a rotating charged ModMax black hole,” Commun. Theor. Phys.76, 025401 (2024)

    2024

  31. [31]

    Light rings and shadows of static black holes in effective quantum gravity,

    Wentao Liu, Di Wu, and Jieci Wang, “Light rings and shadows of static black holes in effective quantum gravity,” Phys. Lett. B858, 139052 (2024), arXiv:2408.05569 [gr-qc]

    Pith/arXiv arXiv 2024

  32. [32]

    Kerr-MOG-(A)dS black hole and its shadow in scalar-tensor-vector gravity theory,

    Wentao Liu, Di Wu, Xiongjun Fang, Jiliang Jing, and Jieci Wang, “Kerr-MOG-(A)dS black hole and its shadow in scalar-tensor-vector gravity theory,” JCAP08, 035 (2024), arXiv:2406.00579 [gr-qc]

    Pith/arXiv arXiv 2024

  33. [33]

    Absorption, Scattering, Geodesics, Shadows and Lensing Phenomena of Black Holes in Effective Quantum Gravity,

    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,” (2024), arXiv:2410.08246 [gr-qc]

    Pith/arXiv arXiv 2024

  34. [34]

    First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,

    Kazunori Akiyamaet al.(Event Horizon Telescope), “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,” Astrophys. J. Lett.875, L1 (2019), arXiv:1906.11238 [astro-ph.GA]

    Pith/arXiv arXiv 2019

  35. [35]

    First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way,

    Kazunori Akiyamaet al.(Event Horizon Telescope), “First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way,” Astrophys. J. Lett.930, L12 (2022), 14 arXiv:2311.08680 [astro-ph.HE]

    Pith/arXiv arXiv 2022

  36. [36]

    Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A,

    Sunny Vagnozziet al., “Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A,” Class. Quant. Grav.40, 165007 (2023), arXiv:2205.07787 [gr-qc]

    Pith/arXiv arXiv 2023

  37. [37]

    Viewing the shadow of the black hole at the galactic center,

    Heino Falcke, Fulvio Melia, and Eric Agol, “Viewing the shadow of the black hole at the galactic center,” Astrophys. J. Lett.528, L13 (2000), arXiv:astro-ph/9912263

    Pith/arXiv arXiv 2000

  38. [38]

    Black Hole Parameter Estimation from Its Shadow,

    Rahul Kumar and Sushant G. Ghosh, “Black Hole Parameter Estimation from Its Shadow,” Astrophys. J.892, 78 (2020), arXiv:1811.01260 [gr-qc]

    Pith/arXiv arXiv 2020

  39. [39]

    Cosmological con- stant corrections to the photon sphere and black hole shadow radii,

    Stephen L. Adler and K. S. Virbhadra, “Cosmological con- stant corrections to the photon sphere and black hole shadow radii,” Gen. Rel. Grav.54, 93 (2022), arXiv:2205.04628 [gr- qc]

    Pith/arXiv arXiv 2022

  40. [40]

    Understanding photon sphere and black hole shadow in dynamically evolving spacetimes,

    Akash K. Mishra, Sumanta Chakraborty, and Sudipta Sarkar, “Understanding photon sphere and black hole shadow in dynamically evolving spacetimes,” Phys. Rev. D99, 104080 (2019), arXiv:1903.06376 [gr-qc]

    Pith/arXiv arXiv 2019

  41. [42]

    Shadows of Kerr–Vaidya-like black holes,

    Hai Siong Tan, “Shadows of Kerr–Vaidya-like black holes,” Class. Quant. Grav.40, 195010 (2023), arXiv:2301.04967 [gr-qc]

    Pith/arXiv arXiv 2023

  42. [43]

    Dynamical fea- tures and shadows of quantum Schwarzschild black hole in effective field theories of gravity,

    Zi-Liang Wang and Emmanuele Battista, “Dynamical fea- tures and shadows of quantum Schwarzschild black hole in effective field theories of gravity,” Eur. Phys. J. C85, 304 (2025), arXiv:2501.14516 [gr-qc]

    Pith/arXiv arXiv 2025

  43. [44]

    Nonstatic Solutions of Einstein’s Field Equa- tions for Spheres of Fluids Radiating Energy,

    P. C. Vaidya, “Nonstatic Solutions of Einstein’s Field Equa- tions for Spheres of Fluids Radiating Energy,” Phys. Rev. 83, 10–17 (1951)

    1951

  44. [45]

    Vaidya’s Radiating Schwarzschild Metric,

    R. W. Lindquist, R. A. Schwartz, and C. W. Misner, “Vaidya’s Radiating Schwarzschild Metric,” Phys. Rev.137, B1364–B1368 (1965)

    1965

  45. [46]

    Vaidya’s Radiating Schwarzschild Metric,

    R. W. Lindquist, R. A. Schwartz, and C. W. Misner, “Vaidya’s Radiating Schwarzschild Metric,” Physical Review 137, 1364–1368 (1965)

    1965

  46. [47]

    Revisiting Vaidya Horizons,

    Alex B. Nielsen, “Revisiting Vaidya Horizons,” Galaxies2, 62–71 (2014)

    2014

  47. [48]

    Dynamical sur- face gravity,

    Alex B. Nielsen and Jong Hyuk Yoon, “Dynamical sur- face gravity,” Class. Quant. Grav.25, 085010 (2008), arXiv:0711.1445 [gr-qc]

    Pith/arXiv arXiv 2008

  48. [49]

    Vaidya spacetime in the diagonal coordinates,

    V. A. Berezin, V. I. Dokuchaev, and Yu. N. Eroshenko, “Vaidya spacetime in the diagonal coordinates,” J. Exp. Theor. Phys.124, 446–458 (2017), arXiv:1704.06889 [gr-qc]

    Pith/arXiv arXiv 2017

  49. [50]

    Charged black holes in Vaidya backgrounds: Hawking’s Radiation,

    Ng. Ibohal and L. Kapil, “Charged black holes in Vaidya backgrounds: Hawking’s Radiation,” Int. J. Mod. Phys. D 19, 437–464 (2010), arXiv:1001.2616 [gr-qc]

    Pith/arXiv arXiv 2010

  50. [51]

    First analytical calculation of black hole shadow in McVit- tie metric,

    Oleg Yu. Tsupko and Gennady S. Bisnovatyi-Kogan, “First analytical calculation of black hole shadow in McVit- tie metric,” Int. J. Mod. Phys. D29, 2050062 (2020), arXiv:1912.07495 [gr-qc]

    Pith/arXiv arXiv 2020

  51. [52]

    Black hole shadow in an expanding universe with a cosmological constant,

    Volker Perlick, Oleg Yu. Tsupko, and Gennady S. Bisnovatyi- Kogan, “Black hole shadow in an expanding universe with a cosmological constant,” Phys. Rev. D97, 104062 (2018), arXiv:1804.04898 [gr-qc]

    Pith/arXiv arXiv 2018

  52. [53]

    The shadow of a collapsing dark star,

    Stefanie Schneider and Volker Perlick, “The shadow of a collapsing dark star,” Gen. Rel. Grav.50, 58 (2018), arXiv:1802.04901 [gr-qc]

    Pith/arXiv arXiv 2018

  53. [54]

    Dynamical photon sphere and time evolving shadow around black holes with temporal accretion,

    Yasutaka Koga, Nobuyuki Asaka, Masashi Kimura, and Kazumasa Okabayashi, “Dynamical photon sphere and time evolving shadow around black holes with temporal accretion,” Phys. Rev. D105, 104040 (2022), arXiv:2202.00201 [gr-qc]

    Pith/arXiv arXiv 2022

  54. [55]

    Generalized Vaidya solu- tions,

    Anzhong Wang and Yumei Wu, “Generalized Vaidya solu- tions,” Gen. Rel. Grav.31, 107 (1999), arXiv:gr-qc/9803038

    Pith/arXiv arXiv 1999

  55. [56]

    Exact solutions for null fluid collapse,

    Viqar Husain, “Exact solutions for null fluid collapse,” Phys. Rev. D53, 1759–1762 (1996), arXiv:gr-qc/9511011

    Pith/arXiv arXiv 1996

  56. [57]

    Radiation and string atmo- sphere for relativistic stars,

    E. N. Glass and J. P. Krisch, “Radiation and string atmo- sphere for relativistic stars,” Phys. Rev. D57, 5945–5947 (1998), arXiv:gr-qc/9803040

    Pith/arXiv arXiv 1998

  57. [58]

    Two fluid atmosphere for relativistic stars,

    E. N. Glass and J. P. Krisch, “Two fluid atmosphere for relativistic stars,” Class. Quant. Grav.16, 1175–1184 (1999), arXiv:gr-qc/9901034

    Pith/arXiv arXiv 1999

  58. [59]

    Gravitational collapse of generalized Vaidya space- time,

    Maombi D. Mkenyeleye, Rituparno Goswami, and Sunil D. Maharaj, “Gravitational collapse of generalized Vaidya space- time,” Phys. Rev. D90, 064034 (2014), arXiv:1407.4309 [gr-qc]

    Pith/arXiv arXiv 2014

  59. [60]

    The eternal naked singularity formation in the case of gravitational collapse of generalized Vaidya space–time,

    Vitalii Vertogradov, “The eternal naked singularity formation in the case of gravitational collapse of generalized Vaidya space–time,” Int. J. Mod. Phys. A33, 1850102 (2018), arXiv:2210.16131 [gr-qc]

    Pith/arXiv arXiv 2018

  60. [61]

    Naked singularity formation in gen- eralized Vaidya space-time,

    V. D. Vertogradov, “Naked singularity formation in gen- eralized Vaidya space-time,” Grav. Cosmol.22, 220–223 (2016)

    2016

  61. [62]

    The structure of the generalized Vaidya space–time containing the eternal naked singularity,

    Vitalii Vertogradov, “The structure of the generalized Vaidya space–time containing the eternal naked singularity,” Int. J. Mod. Phys. A37, 2250185 (2022), arXiv:2209.10953 [gr-qc]

    Pith/arXiv arXiv 2022

  62. [63]

    Collapsing scenario for the k-essence emergent generalized Vaidya spacetime in the context of massive gravity’s rainbow,

    Saibal Ray, Arijit Panda, Bivash Majumder, Md. Rabiul Islam, and Goutam Manna, “Collapsing scenario for the k-essence emergent generalized Vaidya spacetime in the context of massive gravity’s rainbow,” Chin. Phys. C46, 125103 (2022), arXiv:2208.05778 [gr-qc]

    Pith/arXiv arXiv 2022

  63. [64]

    Gravitational Collapse of Baryonic and Dark matter,

    Dipanjan Dey and Pankaj S. Joshi, “Gravitational Collapse of Baryonic and Dark matter,” Arab. J. Math.8, 269–292 (2019), arXiv:1907.12738 [gr-qc]

    Pith/arXiv arXiv 2019

  64. [65]

    Radiating stars with generalised Vaidya atmospheres,

    S. D. Maharaj, G. Govender, and M. Govender, “Radiating stars with generalised Vaidya atmospheres,” Gen. Rel. Grav. 44, 1089–1099 (2012), arXiv:1301.1417 [gr-qc]

    Pith/arXiv arXiv 2012

  65. [66]

    Generalized Vaidya spacetime: Horizons, conformal symmetries, sur- face gravity and diagonalization,

    Vitalii Vertogradov and Dmitriy Kudryavcev, “Generalized Vaidya spacetime: Horizons, conformal symmetries, sur- face gravity and diagonalization,” Mod. Phys. Lett. A38, 2350119 (2023), arXiv:2212.07130 [gr-qc]

    Pith/arXiv arXiv 2023

  66. [67]

    The generalized Vaidya spacetime with polytropic equation of state,

    Vitalii Vertogradov, “The generalized Vaidya spacetime with polytropic equation of state,” Gen. Rel. Grav.56, 59 (2024), arXiv:2311.15671 [gr-qc]

    Pith/arXiv arXiv 2024

  67. [68]

    Vaidya and Gen- eralized Vaidya Solutions by Gravitational Decoupling,

    Vitalii Vertogradov and Maxim Misyura, “Vaidya and Gen- eralized Vaidya Solutions by Gravitational Decoupling,” Uni- verse8, 567 (2022), arXiv:2209.07441 [gr-qc]

    Pith/arXiv arXiv 2022

  68. [69]

    The Negative Energy in Gen- eralized Vaidya Spacetime,

    Vitalii Vertogradov, “The Negative Energy in Gen- eralized Vaidya Spacetime,” Universe6, 155 (2020), arXiv:2209.10976 [gr-qc]

    Pith/arXiv arXiv 2020

  69. [70]

    Surrounded Vaidya solution by cosmological fields,

    Y. Heydarzade and F. Darabi, “Surrounded Vaidya solution by cosmological fields,” Eur. Phys. J. C78, 582 (2018), arXiv:1710.04485 [gr-qc]

    Pith/arXiv arXiv 2018

  70. [71]

    Surrounded Vaidya black holes: apparent horizon properties,

    Y. Heydarzade and F. Darabi, “Surrounded Vaidya black holes: apparent horizon properties,” Eur. Phys. J. C78, 342 (2018), arXiv:1805.01022 [gr-qc]

    Pith/arXiv arXiv 2018

  71. [72]

    Surrounded Bonnor–Vaidya solution by cosmological fields,

    Y. Heydarzade and F. Darabi, “Surrounded Bonnor–Vaidya solution by cosmological fields,” Eur. Phys. J. C78, 1004 (2018)

    2018

  72. [73]

    Analyzing the influ- ence of geometrical deformation on photon sphere and shadow radius: A new analytical approach — Spherically symmetric spacetimes,

    Vitalii Vertogradov and Ali ¨Ovg¨ un, “Analyzing the influ- ence of geometrical deformation on photon sphere and shadow radius: A new analytical approach — Spherically symmetric spacetimes,” Phys. Dark Univ.45, 101541 (2024), arXiv:2404.04046 [gr-qc]. 15

    Pith/arXiv arXiv 2024

  73. [74]

    General approach on shadow radius and photon spheres in asymptotically flat spacetimes and the impact of mass-dependent variations,

    Vitalii Vertogradov and Ali ¨Ovg¨ un, “General approach on shadow radius and photon spheres in asymptotically flat spacetimes and the impact of mass-dependent variations,” Phys. Lett. B854, 138758 (2024), arXiv:2404.18536 [gr-qc]

    Pith/arXiv arXiv 2024

  74. [75]

    Does a primary hair have an impact on the naked singularity formation in hairy Vaidya spacetime? ,

    Vitalii Vertogradov, “Does a primary hair have an impact on the naked singularity formation in hairy Vaidya spacetime? ,” Physics of Complex Systems5, 8390 (2024)

    2024

  75. [76]

    Influence of primary hair and plasma on intensity distribution of black hole shadows,

    Vitalii Vertogradov, Maxim Misyura, and Parth Bambhaniya, “Influence of primary hair and plasma on intensity distribution of black hole shadows,” (2024), arXiv:2403.16743 [gr-qc]

    Pith/arXiv arXiv 2024

  76. [78]

    Barotropic Equation of State and Nonlinear Electrodynamics in Dy- namical Black Hole Spacetimes,

    Vitalii Vertogradov and Dmitriy Kudryavtcev, “Barotropic Equation of State and Nonlinear Electrodynamics in Dy- namical Black Hole Spacetimes,” International Journal of Geometric Methods in Modern Physics23, 2550303 (2025), arXiv:2504.20882 [gr-qc]

    Pith/arXiv arXiv 2025

  77. [79]

    Photon sphere and shadow of a time-dependent black hole described by a Vaidya metric,

    Jay Solanki and Volker Perlick, “Photon sphere and shadow of a time-dependent black hole described by a Vaidya metric,” Phys. Rev. D105, 064056 (2022), arXiv:2201.03274 [gr-qc]

    Pith/arXiv arXiv 2022

  78. [80]

    Dynamical photon spheres in charged black holes and naked singular- ities,

    Yaghoub Heydarzade and Vitalii Vertogradov, “Dynamical photon spheres in charged black holes and naked singular- ities,” Eur. Phys. J. C84, 582 (2024), arXiv:2311.08930 [gr-qc]

    Pith/arXiv arXiv 2024