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arxiv: 2510.25973 · v2 · submitted 2025-10-29 · 🌀 gr-qc · hep-th

Spin effects on particle creation and evaporation in f(R,T) gravity

A. A. Ara\'ujo Filho , N. Heidari , Francisco S. N. Lobo This is my paper

Pith reviewed 2026-05-18 02:52 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords f(R,T) gravityblack hole evaporationparticle creationgreybody factorsspin effectsabsorption cross sectionHawking radiationquasinormal modes
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The pith

Spin of particle modes changes creation and evaporation of black holes in f(R,T) gravity.

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

The paper investigates how particle spin influences particle creation, greybody factors, absorption, and evaporation for black holes in the framework of modified electrodynamics within f(R,T) gravity. It examines massless bosonic and fermionic perturbations across scalar, vector, tensor, and spinorial sectors to derive spin-dependent particle densities and analytical or approximate greybody factors. Absorption cross sections are computed numerically, and the Stefan-Boltzmann law is applied to estimate evaporation lifetimes along with emission rates and the relation to quasinormal modes. A sympathetic reader would care because these differences could produce observable signatures that distinguish this modified gravity model from standard general relativity through quantum radiation processes.

Core claim

By analyzing the wave equations for massless perturbations of different spins on the black hole background in f(R,T) gravity, the authors derive the corresponding particle creation densities and greybody factors. Suitable approximations are used for the tensor and spinorial cases, the absorption cross section is evaluated numerically, and the Stefan-Boltzmann law yields estimates for the black hole evaporation lifetime, with discussion of energy and particle emission rates plus the correspondence between quasinormal modes and greybody factors.

What carries the argument

Spin-dependent greybody factors and absorption cross sections derived from the perturbation equations for scalar, vector, tensor, and spinorial fields on the f(R,T) black hole background.

If this is right

  • Greybody factors and transmission probabilities differ across scalar, vector, tensor, and spinorial modes.
  • Absorption cross sections vary with spin and can be obtained numerically for each sector.
  • Black hole evaporation lifetimes and emission rates depend on the spin of the particles involved.
  • Quasinormal modes exhibit a direct correspondence with the features of the greybody factors.

Where Pith is reading between the lines

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

  • These spin-dependent effects could provide a route to test f(R,T) gravity via precision observations of Hawking radiation from astrophysical black holes.
  • The approach might generalize to other modified gravity models to identify common or distinguishing patterns in quantum field behavior on curved backgrounds.
  • Including massive fields or backreaction effects could extend the evaporation estimates toward more realistic astrophysical scenarios.

Load-bearing premise

The black-hole background solution and the modified electrodynamics coupling are taken directly from the specific f(R,T) model, and this must be physically realized for the spin-dependent rates to hold.

What would settle it

A measurement of black hole particle emission spectra showing no spin dependence in greybody factors or evaporation lifetimes, or a mismatch with the predicted numerical absorption cross sections, would falsify the central results.

Figures

Figures reproduced from arXiv: 2510.25973 by A. A. Ara\'ujo Filho, Francisco S. N. Lobo, N. Heidari.

Figure 1
Figure 1. Figure 1: The particle density for fermions nψ is shown against the frequency ω. On the left panel, we consider the variation of Q for fixed values of α = β = −0.001. On the right panel, we vary α = β for a fixed value of Q = 0.9. Q α = β nψ Q α = β nψ 0.60 -0.01 0.07278720 0.99 -0.01 0.00334425 0.70 -0.01 0.07010770 0.99 -0.02 0.00369590 0.80 -0.01 0.06413920 0.99 -0.03 0.00407625 0.90 -0.01 0.04879970 0.99 -0.04 0… view at source ↗
Figure 2
Figure 2. Figure 2: The greybody factors for spin–0 particle modes are presented for fixed values of α = β = −0.01, considering various values of Q and angular momentum number ℓ. The top left panel corresponds to ℓ = 0, the top right panel displays the case ℓ = 1, and the bottom panel shows the results for ℓ = 2. one corresponds to ℓ = 1, and the bottom panel depicts the scenario for ℓ = 2. Notice that the reduction ascribed … view at source ↗
Figure 3
Figure 3. Figure 3: The greybody factors for spin–0 particle modes are presented for fixed values of Q = 0.9, considering various values of α = β and angular momentum number ℓ. The top left panel corresponds to ℓ = 0, the top right panel displays the case ℓ = 1, and the bottom panel shows the results for ℓ = 2. where ˜ζ = −400M3Q2p (M − Q)(M + Q) + 260M2Q4 + 100MQ4p (M − Q)(M + Q) − Q4 (−2αβ + α + 20Q2 ). To interpret the res… view at source ↗
Figure 4
Figure 4. Figure 4: The greybody factors corresponding to spin–1 particle modes are shown for α = β = −0.01, with different values of the charge Q and the angular momentum quantum number ℓ. The left and right panels represent the cases ℓ = 1, and ℓ = 2, respectively. 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 -2.0 -1.5 -1.0 -0.5 0. 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 -2.0 -1.5 -1.0 -0.5 0 [PITH_FULL_IMAGE:figures/full_fig_p029_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The greybody factors for spin–1 particle modes are displayed for a fixed charge Q = 0.9, while varying the parameters α = β and the angular momentum number ℓ. The left panel depicts the case where ℓ = 1, and the right panel presents the results for ℓ = 2. C. Spin–2 particle modes In this section, we present the computation of the greybody factors associated with tensor perturbations. Unlike the previous an… view at source ↗
Figure 6
Figure 6. Figure 6: The greybody factors associated with spin–2 particle modes are shown for α = β = −0.01, while the parameters Q and the angular momentum number ℓ are varied. The top left panel illustrates the configuration with ℓ = 2, the top right one depicts ℓ = 3, and the lower panel presents the corresponding results for ℓ = 4. D. Spin–1/2 particle modes Now, the investigation of the greybody factors ends by addressing… view at source ↗
Figure 7
Figure 7. Figure 7: The greybody factors for spin–1/2 modes are displayed for α = β = −0.01, while varying the charge Q and the angular momentum quantum number ℓ. The upper left, upper right, and lower panels correspond to ℓ = 1/2, ℓ = 3/2, and ℓ = 5/2, respectively. α = β (for a fixed value of Q) due to dificult in distinghising the different lines. Nevertheless, as α = β decreases, the corresponding magnitude of the associd… view at source ↗
Figure 8
Figure 8. Figure 8: The comparison of the greybody factors as functions of the frequency ω is carried out for all perturbations considered—scalar (|T S b |), vector (|T V b |), tensor (|T T b |), and spinorial (|T ψ b |)—with the parameters fixed at M = 1, ℓ = 2 (for bosonic case), ℓ = 5/2 (for the spinor case),Q = 0.1, and α = β = −0.01. VI. ABSORPTION CROSS SECTION In this section, we analyze the scattering behavior of the … view at source ↗
Figure 9
Figure 9. Figure 9: The absorption cross sections for spin–0 particle modes are shown for a fixed mass parameter M = 1, evaluated across different values of α, β, Q, and the angular momentum number ℓ. The top left and right panels correspond to ℓ = 1, while the bottom panel presents the results for Q = 0.5 with α = β = −0.1. values of the deformation parameters α = β (from 0.0 down to −2.0) lead to a substantial increase in t… view at source ↗
Figure 10
Figure 10. Figure 10: Absorption cross sections for the vector field are plotted for a fixed mass parameter M = 1, considering different values of α, β, Q, and the angular momentum ℓ. The top panels correspond to ℓ = 1, and the bottom panel shows the case Q = 0.5 with α = β = −0.1. B. Spin–1 particle modes The absorption cross sections for spin–1 fields are presented in [PITH_FULL_IMAGE:figures/full_fig_p037_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The absorption cross sections for tensor (spin–2) field modes are presented for a fixed black hole mass parameter M = 1. The results are computed for different values of the parameters α, β, Q, and the angular momentum number ℓ. The top panels correspond to ℓ = 2, while the bottom panel illustrates the case Q = 0.5 with α = β = −0.1. momentum number ℓ. As expected, larger ℓ values suppress the overall mag… view at source ↗
Figure 12
Figure 12. Figure 12: Fermionic absorption cross sections for the case M = 1. Top Left: Variation with α and β for ℓ = 1 and different Q. Top panels: A complementary view of the parameter space for ℓ = 1. Bottom panel: Dependence on the multipole number ℓ for a fixed configuration with Q = 0.5 and α = β = −0.1. progressively constructed from the contributions of higher angular momentum modes. We now present a unified compariso… view at source ↗
Figure 13
Figure 13. Figure 13: The comparison of the absorption cross section as functions of the frequency ω is presented for all spin types 0, 1/2, 1, 2. The σ S abs, σ T abs, σ V abs, σ ψ abs are denoted to scalar, vector, tensor, and spinorial perturbations, respectively. The values are set to M = 1, Q = 0.1 and α = β = −0.01. The angular momentum for bosonic and fermionic cases is fixed at ℓ = 2 and ℓ = 5/2, respectively. Γ¯ψ ℓω (… view at source ↗
Figure 14
Figure 14. Figure 14: The energy emission rate for spin-0 particle modes is displayed. The left panel shows the dependence on the charge Q with M = 1 and α = β = −0.01, while the right panel displays the variation with α = β for fixed M = 1 and Q = 0.9. Here, we consider ℓ = 2. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 1×10-6 2×10-6 3×10-6 4×10-6 5×10-6 0. 0.1 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 0.6 0.7 0 5.0×10-8 1.0×10-7 1.5×10-7 -0.30 … view at source ↗
Figure 15
Figure 15. Figure 15: The particle emission rate for spin–0 modes is shown. The left panel illustrates how the spectrum varies with Q when M = 1 and α = β = −0.01, whereas the right panel depicts the effect of changing α = β while keeping M = 1 and Q = 0.9 constant. Here, we consider ℓ = 2. ω fixed. Second, decreasing α = β with Q and ω fixed also shortens the lifetime. Third, higher frequencies ω enhance the emission power, c… view at source ↗
Figure 16
Figure 16. Figure 16: The energy emission rate for spin–1 particle modes is displayed. The left panel shows the dependence on the charge Q with M = 1 and α = β = −0.01, while the right panel displays the variation with α = β for fixed M = 1 and Q = 0.9. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 1×10-6 2×10-6 3×10-6 4×10-6 [PITH_FULL_IMAGE:figures/full_fig_p046_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The comparison of the energy emission rates is shown for spin–0 and spin–1 cases with α = β = −0.01, M = 1, Q = 0.1, and ℓ = 2. particle emission rate. As in the scalar case, increasing Q leads to a reduction in the emission rate, whereas decreasing α = β produces a slight enhancement. Moreover, following the same procedure adopted for the energy emission, we now com￾pare the results for the particle emis… view at source ↗
Figure 18
Figure 18. Figure 18: The particle emission rate for spin–1 modes is shown. The left panel illustrates how the spectrum varies with Q when M = 1 and α = β = −0.01, whereas the right panel depicts the effect of changing α = β while keeping M = 1 and Q = 0.9 constant. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.00000 2×10-6 4×10-6 6×10-6 8×10-6 0.00001 [PITH_FULL_IMAGE:figures/full_fig_p047_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: The comparison of the particle emission rates is exhibited for spin–0 and spin–1 cases with α = β = −0.01, M = 1, Q = 0.1, and ℓ = 2. C. Spin–2 particle modes We shall devote our attention to investigate how the spin–2 particle are emitted from our black hole under consideration. Initially, as we have accopmlished in our previous sections, we shall begin by studying the evaporation lifetime associated to … view at source ↗
Figure 20
Figure 20. Figure 20: The energy emission rate for spin-2 particle modes is displayed. The left panel shows the dependence on the charge Q with M = 1 and α = β = −0.01, while the right panel displays the variation with α = β for fixed M = 1 and Q = 0.9. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.00000 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012 0.2 0.4 0.6 0.8 1.0 1.2 0 1×10-6 2×10-6 3×10-6 4×10-6 5×10-6 6×10-6 7×10-6 [PITH_FULL_I… view at source ↗
Figure 21
Figure 21. Figure 21: The particle emission rate for spin–2 modes is shown. The left panel illustrates how the spectrum varies with Q when M = 1 and α = β = −0.01, whereas the right panel depicts the effect of changing α = β while keeping M = 1 and Q = 0.9 constant. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.00000 0.00001 0.00002 0.00003 0.00004 [PITH_FULL_IMAGE:figures/full_fig_p050_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: The comparison of the particle emission rates is exhibited for spin–0, spin–1 and spin–2 cases with α = β = −0.01, M = 1, Q = 0.1, and ℓ = 2. 50 [PITH_FULL_IMAGE:figures/full_fig_p050_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: The energy emission rate for spin–1/2 particle modes is displayed. The left panel shows the dependence on the charge Q with M = 1 and α = β = −0.01, while the right panel displays the variation with α = β for fixed M = 1 and Q = 0.9. Here, we consider ℓ = 5/2. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 5.0×10-8 1.0×10-7 1.5×10-7 2.0×10-7 2.5×10-7 0.2 0.4 0.6 0.8 1.0 0 1×10-9 2×10-9 3×10-9 4×10-9 [PITH_FULL_IMAGE:… view at source ↗
Figure 24
Figure 24. Figure 24: The particle emission rate for spin–1/2 modes is shown. The left panel illustrates how the spectrum varies with Q when M = 1 and α = β = −0.01, whereas the right one depicts the effect of changing α = β while keeping M = 1 and Q = 0.9 constant. Here, we regard ℓ = 5/2. Bose–Einstein statistics, can share the same quantum state, which amplifies their collective emission rate. Fermions, on the other hand, o… view at source ↗
Figure 25
Figure 25. Figure 25: The comparison of all the energy emission rates regarding spin–0, spin–1, spin–2, and spin–1/2 cases with α = β = −0.01, M = 1, Q = 0.1, and ℓ = 2 (for bosons) and ℓ = 5/2 (for fermions). limiting value of the absorption cross section, σℓω → σlim, approaches πR2 , where R denotes the shadow radius associated with the black hole geometry [32] R = vuuuut  γ + 1 2 p 9M2 − 8Q2 + 3M 2 Q2  γ+ 1 2 √ 9M2−8Q… view at source ↗
Figure 26
Figure 26. Figure 26: In the high–energy regime, the final evaporation time tevap-final, obtained in the limit Mf → Mrem, is depicted as a function of the initial mass Mi . The left panel illustrates the dependence on different charge values Q for fixed α = β = −0.01, whereas the right panel presents the variation with α = β for a constant charge Q = 0.9. mass over time—a process known as Hawking radiation, as previously outli… view at source ↗
Figure 27
Figure 27. Figure 27: Energy emission rate in the high–energy regime. The left panel shows the dependence of the spectrum on the charge Q for fixed parameters M = 1 and α = β = −0.01, while the right one displays the variation with α = β at fixed M = 1 and Q = 0.9. 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.5 1.0 1.5 0. 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0 -0.30 -0.25 -0.20 -0.15 -0.10 [PITH_FULL_IMAGE:figur… view at source ↗
Figure 28
Figure 28. Figure 28: The particle emission rate for high energy limit case is shown. The left panel illustrates how the spectrum varies with Q when M = 1 and α = β = −0.01, whereas the right one depicts the effect of changing α = β while keeping M = 1 and Q = 0.9 constant. VIII. THE CORRESPONDENCE OF QNMS AND GREYBODY FACTORS The quasinormal mode frequencies can be efficiently estimated using the semi–analytical WKB method. O… view at source ↗
Figure 29
Figure 29. Figure 29: Correlation between quasinormal modes and greybody factors for scalar perturbations, evaluated with α = β = −0.01 and angular momentum number ℓ = 1. and ∆f = − (ω 2 − ω 2 0R) 3 32ω 5 0Rω0I ( 1 + ω0R(ω0R − ω1R) 4ω0I 2 + ω 2 0R " (ω0R − ω1R) 2 16ω 4 0I − 3ω0I − ω1I 12ω0I #) . (122) In what follows, the developed formalism is employed to evaluate the greybody factors corresponding to scalar, vector, tensor, … view at source ↗
Figure 30
Figure 30. Figure 30: The profile of the scalar effective potential VS(r, α, β, Q) is plotted against the radial coordinate r, considering M = 1, ℓ = 1, and α = β = −0.01, for various choices of the charge parameter Q. B. Spin–1 particle modes [PITH_FULL_IMAGE:figures/full_fig_p060_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Correlation between quasinormal modes and greybody factors for vector perturbations, evaluated with parameters α = β = −0.01 and angular momentum number ℓ = 1. 0 2 4 6 8 10 0.00 0.02 0.04 0.06 0.08 0.10 0.12 [PITH_FULL_IMAGE:figures/full_fig_p061_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: The variation of the vector effective potential VV(r, α, β, Q) with respect to the radial coordinate r is presented for several charge values Q, considering the fixed parameters M = 1, ℓ = 1, and α = β = −0.01. resulting in stronger wave reflection and greater suppression of oscillatory behavior. D. Spin–1/2 particle modes [PITH_FULL_IMAGE:figures/full_fig_p061_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Relation between quasinormal modes and greybody factors for tensor perturbations, evaluated with parameters α = β = −0.01 and angular momentum number ℓ = 2. 0 2 4 6 8 10 0.00 0.05 0.10 0.15 0.20 [PITH_FULL_IMAGE:figures/full_fig_p062_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: The dependence of the tensor effective potential VT(r, α, β, Q) on the radial coordinate r is illustrated for several charge values Q, with the fixed parameters M = 1, ℓ = 2, and α = β = −0.01. the quasinormal mode spectrum reported in Ref. [32], where increasing Q leads to stronger damping. In this situation, the rise in Q enhances the effective potential barrier (see [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 35
Figure 35. Figure 35: Connection between quasinormal modes and greybody factors for spinor perturbations, obtained for α = β = −0.01 and angular momentum number ℓ = 5/2. 2 4 6 8 10 12 14 0.0 0.1 0.2 0.3 0.4 [PITH_FULL_IMAGE:figures/full_fig_p063_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: The radial profile of the spinorial effective potential Vψ(r, α, β, Q) is plotted for several charge values Q, taking fixed parameters M = 1, ℓ = 5/2, and α = β = −0.01. tors, absorption cross sections, and evaporation—within the framework of f(R, T) gravity coupled to a modified electrodynamics. The analysis was motivated by the quest to un￾derstand how modifications of the underlying gravitational and e… view at source ↗
read the original abstract

In this work, we study how the spin of particle modes influences particle creation, greybody factors, absorption, and evaporation of a black hole within the framework of modified electrodynamics in $f(R,T)$ gravity, recently proposed in Ref. [1]. All spin sectors -- scalar, vector, tensor, and spinorial -- are analyzed to obtain the corresponding features. For particle creation, we consider massless bosonic and fermionic perturbations to determine the respective particle densities. Analytical expressions for the greybody factors are derived, with suitable approximations for the tensor and spinorial cases. The absorption cross section is computed numerically, and using the Stefan-Boltzmann law, we estimate the black hole evaporation lifetime. The associated energy and particle emission rates are also discussed, along with the correspondence between quasinormal modes and greybody factors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper studies the influence of particle spin on creation rates, greybody factors, absorption cross-sections, and evaporation lifetimes for a black hole in f(R,T) gravity. It analyzes scalar, vector, tensor, and spinorial modes for massless bosonic and fermionic perturbations, derives analytical greybody factor expressions (with approximations for tensor and spinorial cases), computes numerical absorption cross sections, estimates evaporation lifetimes via the Stefan-Boltzmann law, and discusses energy/particle emission rates together with the quasinormal mode-greybody correspondence, all on a background taken from Ref. [1].

Significance. If the background metric and couplings are valid and the approximations are controlled, the work would offer concrete spin-dependent predictions for Hawking radiation and evaporation in modified gravity, extending standard GR results to f(R,T) models and potentially yielding observable distinctions in black-hole lifetimes. The numerical absorption computations and analytical greybody expressions constitute a useful technical contribution if properly validated.

major comments (3)
  1. §2 (or equivalent background section): The line element and modified electrodynamics coupling are adopted directly from Ref. [1] with no independent derivation or explicit verification that the metric satisfies the f(R,T) field equations for the stated f(R,T) function. All subsequent spin-sector analyses rest on this background; without a consistency check or re-derivation, the grounding of the particle creation rates and greybody factors is not established within the manuscript.
  2. Greybody factor section (tensor and spinorial approximations): The text states that suitable approximations are used for tensor and spinorial cases, yet no error bounds, validity range, or reduction to the known GR limits (where spin-dependent greybody factors are standard) are supplied. This directly affects the reliability of the claimed analytical expressions and their use in evaporation estimates.
  3. Numerical absorption cross-section and evaporation lifetime section: The absorption cross sections are obtained numerically and fed into Stefan-Boltzmann evaporation lifetimes, but the manuscript reports neither error bars, convergence tests with respect to integration parameters, nor sensitivity to the f(R,T) coupling strength. These omissions undermine the quantitative claims for spin-dependent lifetimes.
minor comments (2)
  1. Abstract: The phrase 'modified electrodynamics in f(R,T) gravity' is used without a brief clarification of how the trace-coupling term enters the perturbation equations; a single clarifying sentence would improve readability.
  2. Notation: The distinction between bosonic and fermionic particle densities is not always explicit when results for different spins are compared; consistent use of subscripts (e.g., s=0,1,2,1/2) throughout would aid clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and outline the revisions we will implement to strengthen the presentation.

read point-by-point responses

  1. Referee: §2 (or equivalent background section): The line element and modified electrodynamics coupling are adopted directly from Ref. [1] with no independent derivation or explicit verification that the metric satisfies the f(R,T) field equations for the stated f(R,T) function. All subsequent spin-sector analyses rest on this background; without a consistency check or re-derivation, the grounding of the particle creation rates and greybody factors is not established within the manuscript.

    Authors: We agree that an explicit consistency check strengthens the foundation. In the revised manuscript we will add a short verification subsection in §2 that substitutes the adopted line element into the f(R,T) field equations for the chosen functional form, confirms the modified electrodynamics coupling, and states the resulting constraints on the parameters. This will be done without repeating the full derivation of Ref. [1] but with sufficient algebraic steps to establish internal consistency. revision: yes

  2. Referee: Greybody factor section (tensor and spinorial approximations): The text states that suitable approximations are used for tensor and spinorial cases, yet no error bounds, validity range, or reduction to the known GR limits (where spin-dependent greybody factors are standard) are supplied. This directly affects the reliability of the claimed analytical expressions and their use in evaporation estimates.

    Authors: We acknowledge the need for quantitative control on the approximations. We will augment the greybody-factor section with (i) explicit error estimates obtained by comparing the approximate analytic expressions to numerical solutions of the radial wave equations over the relevant frequency range, (ii) a statement of the validity domain in terms of the f(R,T) coupling parameter and the multipole index, and (iii) a direct reduction to the standard GR greybody factors in the limit where the f(R,T) corrections vanish. These additions will be supported by a new figure or table summarizing the relative errors. revision: yes

  3. Referee: Numerical absorption cross-section and evaporation lifetime section: The absorption cross sections are obtained numerically and fed into Stefan-Boltzmann evaporation lifetimes, but the manuscript reports neither error bars, convergence tests with respect to integration parameters, nor sensitivity to the f(R,T) coupling strength. These omissions undermine the quantitative claims for spin-dependent lifetimes.

    Authors: We accept that additional numerical validation is required. In the revised version we will include (i) error bars on the absorption cross sections derived from the numerical integration tolerances, (ii) convergence tests with respect to the radial grid spacing and the cutoff frequency, and (iii) a brief sensitivity study showing how the evaporation lifetimes vary with the f(R,T) coupling strength. The updated figures and accompanying text will make these controls explicit. revision: yes

Circularity Check

1 steps flagged

Central results rest on unverified adoption of background metric and coupling from Ref. [1]

specific steps
  1. self citation load bearing [Abstract]
    "In this work, we study how the spin of particle modes influences particle creation, greybody factors, absorption, and evaporation of a black hole within the framework of modified electrodynamics in $f(R,T)$ gravity, recently proposed in Ref. [1]."

    The black-hole background metric, field equations, and trace-coupling to matter are adopted wholesale from Ref. [1] without independent derivation or check against the modified field equations for the chosen perturbations. All analytic expressions for particle densities, greybody factors, numerical absorption cross-sections, and evaporation lifetimes are computed on this imported spacetime, so the central claims reduce to the validity of the cited model.

full rationale

The paper imports the black-hole spacetime and modified electrodynamics coupling directly from Ref. [1] as the foundation for all calculations. The new contributions consist of analyzing spin-dependent perturbations (scalar, vector, tensor, spinorial) on that fixed background, deriving greybody factors, absorption cross-sections, and evaporation rates. This constitutes a self-citation load-bearing step because the validity of every subsequent result hinges on the imported solution satisfying the f(R,T) equations, yet no re-derivation or consistency verification appears in the text. The spin-sector analysis itself is independent and adds content, preventing a higher circularity score. No self-definitional reductions, fitted predictions, or ansatz smuggling are present in the provided derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the validity of the f(R,T) action and black-hole solution from Ref. [1], the semiclassical treatment of massless perturbations, and the applicability of the Stefan-Boltzmann law to the modified Hawking spectrum.

axioms (2)
  • domain assumption The f(R,T) gravity model and its black-hole solution proposed in Ref. [1] correctly describe the spacetime and matter coupling.
    All greybody and evaporation calculations are performed on this background.
  • domain assumption Massless bosonic and fermionic perturbations can be treated with standard wave equations on the curved background.
    Particle creation and greybody factors are obtained from these perturbation equations.

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  2. Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity

    gr-qc 2026-05 unverdicted novelty 4.0

    Perturbative f(R, G) corrections shift the photon-sphere radius and black-hole shadow size, with the Gauss-Bonnet sector contributing more than mixed terms.

  3. Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity

    gr-qc 2026-05 unverdicted novelty 3.0

    Perturbative higher-curvature corrections in f(R,G) gravity shift the photon-sphere radius and black-hole shadow size away from Schwarzschild values, with the Gauss-Bonnet sector contributing more than mixed terms.

Reference graph

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