An atom in front of Lorentz violating Kalb-Ramond black hole background

Anisur Rahaman

REVIEW 4 major objections 5 minor 1 cited by

An atom in front of Lorentz violating Kalb-Ramond black hole background

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A falling atom in a Kalb-Ramond black hole sees Lorentz violation in both the amplitude and the exponential factor of its excitation, a breach of the equivalence principle tied to modified entropy.

desk verdict Core transition probability is actually correct, but the paper's simplified limit, entropy section, and l definition are too sloppy for publication. read the letter →

arxiv 2506.01006 v1 pith:FMQANQO6 submitted 2025-06-01 hep-th gr-qc

Anisur Rahaman This is my paper

classification hep-thgr-qc MSC 83C5783C4781T20 PACS 04.70.-s04.60.-m11.30.Cp

keywords Kalb-RamondblackholeLorentzviolationaccelerationradiationequivalenceprincipleHBARentropytransitionprobabilitythermodynamicstwo-levelatom

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 asks what a falling atom would see while approaching a Kalb-Ramond black hole, a spherically symmetric spacetime whose antisymmetric tensor field spontaneously breaks Lorentz symmetry. Working in a near-horizon uniformly accelerated frame, it derives the atom's excitation and absorption probabilities and finds that both the overall amplitude and the exponential factor of thermal form, $1/(e^{4\pi\nu/A'(r_e)}-1)$, depend on the Lorentz-violating parameter $l$, not only on the black hole mass. Because the spectrum of a uniformly accelerated detector normally encodes only the local acceleration, this $l$-dependence means the radiation carries information about the symmetry-breaking background; the paper interprets that as a breach of the equivalence principle. The same probabilities are fed into a density-matrix master equation to compute how fast the horizon-brightened acceleration-radiation entropy changes, yielding an $l$-dependent rate that still keeps the structural form of the standard area-law entropy. If the calculation holds, these formulas give concrete signatures of Lorentz violation in both the radiation of infalling atoms and black hole thermodynamics.

What carries the argument

The load-bearing mechanism is the near-horizon form of the Kalb-Ramond metric, a Schwarzschild-like spacetime dressed by an antisymmetric tensor field whose vacuum expectation value breaks Lorentz symmetry. Its lapse function $A(r)=1/(1-l)-2GM/(rc^2)$, expanded about the horizon $r_e=2GM(1-l)/c^2$ as $A(r)\simeq(r-r_e)A'(r_e)$, becomes a uniformly accelerated frame with acceleration $a\sim c^2\sqrt{A'(r_e)}/(2\sqrt r)$; the atom's trajectory is then controlled entirely by $A'(r_e)$. Into that geometry the paper inserts the photon mode $e^{-i\nu\int dr/A(r)}$ and evaluates the transition amplitude as a phase integral. The argument is carried by the ratio of excitation to absorption rates, $T_E/T_A=e^{-4\pi\nu/[A'(r_e)]}[1-2\nu/\Omega+\cdots]$, which plugs into the steady-state density matrix whose von Neumann entropy yields the HBAR entropy rate.

What would settle it

The most direct check is to recompute the transition probability from Eq. (42) without the assumption $\Omega\gg A'(r_e),\nu,k$ and without dropping second-order terms in $(r-r_e)$; if the resulting probability does not keep the thermal form $1/(e^{4\pi\nu/A'(r_e)}-1)$, the claimed $l$-dependence is an artifact of the truncation. Alternatively, a future experiment that measures the photon spectrum of an infalling two-level atom near a compact object could compare the excitation-to-absorption ratio against the predicted $l$-dependent detailed-balance form and see whether the effective temperature shifts with the Lorentz-violating parameter.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that Lorentz violation reshapes the radiative response of an infalling atom at two levels at once. Using the near-horizon expansion $A(r)\simeq (r-r_e)A'(r_e)$ with $A'(r_e)=c^2/[2GM(1-l)^2]$, the excitation probability takes the Planck-like form $$P_e \simeq \frac{4\pi $G^{2}$\nu}{A'(r_e)\$\Omega$^2}\left[\left(1-\frac{\nu}{\$\Omega$}\right)^2+\frac{A'^2(r_e)}{4\$\Omega$^2}\right]\frac{1}{$e^{{4\pi\nu/A'(r_e)}}$-1}.$$ The parameter $l$ enters both through the prefactor, via $A'(r_e)$, and through the exponent of the exponential factor, so it rescales the effective temperature of the radiation and the excitation-to-absorption ratio $T_E/T_A\sim e^{-4\pi\nu/[A'(r_e)]}\,[1-2\nu/\Omega+\cdots]$. The paper reads this as a breach of the equivalence principle: a purely local acceleration measurement cannot reproduce a spectrum that depends on the global Lorentz-violating parameter. For the HBAR entropy, the same ratio drives the steady-state density matrix, and the resulting entropy rate carries $l$ in its coefficient while preserving the standard area-law form of black hole entropy; the paper emphasizes that these Kalb-Ramond corrections are quantitatively different from those in bumblebee gravity models.

Load-bearing premise

The formulas stand on the assumptions that the atomic frequency $\Omega$ is much larger than the near-horizon metric slope $A'(r_e)$, the photon frequency $\nu$, and the integration variable $k$, and that keeping only the first-order term in the near-horizon expansion is enough; if either assumption gives way, the closed-form thermal probability and the entropy derived from it do not follow.

Editorial extensions

If this is right

The excitation probability of an infalling atom acquires a thermal factor $1/(e^{4\pi\nu/A'(r_e)}-1)$, so the effective temperature of the radiation is set by $A'(r_e)=c^2/[2GM(1-l)^2]$; a larger Lorentz-violating parameter $l$ means a hotter-looking spectrum for the same black hole mass.
Because $l$ appears in both the prefactor and the exponent of the transition probability, the ratio of excitation to absorption obeys a modified detailed balance, which is the quantitative sense in which the equivalence principle is breached.
The HBAR entropy rate contains an $l$-dependent coefficient and additional $\hbar$-dependent terms, yet it still takes the structural form of the ordinary area-law entropy, giving a computable deviation from general relativity in black hole thermodynamics.
The Kalb-Ramond corrections differ from those of bumblebee gravity, so the two Lorentz-violating models can be distinguished by the pattern of corrections in the falling-atom spectrum rather than only by their overall magnitude.

Reading between the lines

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

The same near-horizon machinery would apply to any metric whose horizon slope differs from Schwarzschild, suggesting a generic template: any parameter that rescales $A'(r_e)$ will show up in both the amplitude and the exponent of the falling-atom spectrum.
A precision measurement of the spectral shape of acceleration radiation near a compact object could constrain $l$ without requiring a full quantum-gravity framework, since the exponent shift is a low-energy observable in the model.
The ordering assumption $\Omega\gg A'(r_e),\nu,k$ confines the result to high-frequency atoms; a future computation in the opposite regime would test whether the equivalence-principle violation survives or is an artifact of the expansion.
The structural resilience of the area-law entropy across different Lorentz-violating mechanisms hints that the area law may be a generic infrared feature, with the symmetry-breaking parameter only reshaping the coefficients.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick read: this applies the Scully et al. atom-falling-into-a-black-hole framework to the Kalb-Ramond metric and computes l-dependent transition probabilities and a modified HBAR entropy. The framework is unchanged; the new piece is plugging the KR metric's A'(r_e) into the known template. That is a legitimate model-level extension, nothing more.

I checked the stress-test's central claim about Eq. (44) because that is load-bearing. The claim does not hold. Using the standard Abel-regularized integral ∫_0^∞ dk k^{z-1} e^{-ik} = Γ(z) e^{-iπz/2}, the integral the paper writes after Eq. (43) evaluates to |I|² = [4πν/(a(e^{4πν/a}-1))] ((1-ν/Ω)² + a²/4Ω²), which is exactly Eq. (44) up to a typo in the intermediate line where G²/Ω² is inside the square instead of outside. So the core transition probability is actually correct.

The soft spots are real, but they are mostly elsewhere. Eq. (45) is wrong as a limit of Eq. (44): the Ω >> A' limit should keep 1/Ω² and keep A' in the denominator, not move it to the numerator. That error is not used later, but it is the kind of thing a referee would catch. The entropy section is the weakest. The TE/TA ratio in Eq. (60) has dimensionally inconsistent correction terms, the function F(A_KR) in Eq. (70) is never written down, and the l parameter is defined twice with different couplings (g1 b²/2 and g0 b²/2). The conclusion also walks back the abstract's strong equivalence-principle claim: the author admits the cause cannot be pinpointed, yet the abstract presents a breach as established. That is an overclaim.

What the paper does well: the derivation is self-contained given the KR metric, the l-dependence of the Planck factor is a concrete signature, and the author engages with the relevant literature; the self-citation to [62] is appropriate as the direct predecessor. The central integral being right gives the paper some value despite the mess.

Recommendation: send to a referee rather than desk reject, because the core calculation is correct and the topic is relevant. But as submitted it should not be published; Eq. (45), the entropy expressions, and the l definition need fixing, and the claims need to match the caveats. I would not cite it in its current form.

Referee Report

4 major / 5 minor

Summary. The manuscript studies a two-level atom falling toward a Kalb-Ramond black hole (metric in Eq. (11)), treated as an Unruh-DeWitt detector. After a near-horizon Rindler reduction, it derives excitation and absorption probabilities, Eqs. (44) and (48), and argues that the Lorentz-violating parameter l enters both the amplitude and the Planck-like exponential, indicating a violation of the equivalence principle. It then uses these probabilities to compute an HBAR entropy rate, Eqs. (60)-(64), and claims that the resulting entropy maintains structural resemblance to Bekenstein-Hawking entropy. The main quantitative claims are the l-dependent transition probability and the entropy formulas.

Significance. If the calculation were correct, the paper would provide a concrete signature of Lorentz violation in KR gravity: a modified prefactor and Planck factor in acceleration radiation, plus an area-dependent entropy expression. The setup is reasonable and the comparison with the bumblebee-gravity treatment [62] is a useful benchmark. However, the central integral in Eq. (44) is evaluated incorrectly, the Planck exponent is dimensionally inconsistent between Eqs. (44) and (60), and the HBAR entropy derivation is not actually carried through to a closed form. These issues are load-bearing, so the significance is conditional on a re-derivation that the present manuscript does not provide.

major comments (4)

[Section IV, Eqs. (43)-(44)] The transition probability is the central quantitative result, but the integral is evaluated incorrectly. For the integrand displayed after Eq. (43), I = \int_0^\infty dk (1 + A' k/(2\Omega)) k^{-2i\nu/A'} e^{-ik}, one obtains |I|^2 = [\pi A'/(\nu(e^{4\pi\nu/A'}-1))] [(1 - \nu/\Omega)^2 + A'^2/(4\Omega^2)]. Inserting the prefactor G^2/\Omega^2 gives P_e = \pi G^2 A'/(\nu\Omega^2(e^{4\pi\nu/A'}-1))[(1 - \nu/\Omega)^2 + A'^2/(4\Omega^2)]. Equation (44) instead states 4\pi G^2\nu/(A'\Omega^2) times the same bracket and Planck factor; the prefactors differ by A'^2/(4\nu^2). The claimed l-dependence of the amplitude is therefore not derived. Moreover Eq. (45) is not the \Omega \gg A' limit of Eq. (44): that limit would be 4\pi G^2\nu/[A'\Omega^2(e^{4\pi\nu/A'}-1)], not 4\pi G^2\nu A'/(e^{4\pi\nu/A'}-1). Finally, the stated assumption \Omega \gg k conflicts with the integration domain k \in [0,\infty), so the asymptotic evaluation is not controlled.
[Section IV, Eqs. (44) and (60)] The Planck exponent is written inconsistently with the units of the metric. In Eq. (44) the exponent is 4\pi\nu/A'(r_e); with A'(r_e)=c^2/[2GM(1-l)^2] this quantity has dimensions of speed, not dimensionless. In Eq. (60) a factor of c is restored, 4\pi\nu/[cA'(r_e)] = 8\pi GM\nu(1-l)^2/c^3. Since the metric (11) contains c explicitly, the transition probability and the entropy formulas must use the same convention; restoring c changes the exponent by a factor c and therefore changes the stated Lorentz-violating dependence of the Planck factor.
[Section V, Eqs. (60)-(64)] The passage from the probabilities to T_E/T_A and to the entropy rate is not substantiated. The ratio T_E/T_A written in Eq. (60), e^{-4\pi\nu/[cA']}[1 - 2\nu/\Omega + (A'^2/\Omega^2)(\nu - 1/4)], does not follow from P_e/P_a computed from Eqs. (44) and (48): the latter ratio contains the factor [(1-\nu/\Omega)^2 + A'^2/(4\Omega^2)] / [(1+\nu/\Omega^2)+A'^2/(4\Omega^2)], and Eq. (48) itself has the dimensionally inconsistent term 1+\nu/\Omega^2. Equation (64) then contains an isolated \nu in the first term, 8\pi GM\nu(1-l)^2/c^3, although the sum over \nu has already been performed through \sum_\nu \dot{\bar n}_\nu \nu; the equation is dimensionally inconsistent. Since the HBAR entropy rate is the paper's second main result, this derivation needs to be redone.
[Section V, Eq. (70)] The paper states that \dot S_\rho = d/dt[F(A_KR)] and that F(A_KR) 'can be easily obtained', but the function F is never exhibited. The abstract's claim that the HBAR entropy in the KR spacetime is 'calculated in detail' is therefore not supported by the manuscript; without F(A_KR), the asserted structural resemblance to Bekenstein-Hawking entropy is uncheckable.

minor comments (5)

[Section II, Eq. (11)] The solution is not asymptotically Minkowski because A(\infty)=1/(1-l); the statement that the solution is 'Asymptotically... flat' is inconsistent with this limit.
[Section IV, Eq. (40)] The displayed formula contains malformed integrals and unexplained symbols (\tilde r, repeated square roots); as written it cannot be checked, and Eq. (42) repeats the problem.
[Section IV, Eq. (48)] The factor (1+\nu/\Omega^2) is dimensionally inconsistent and should presumably be (1+\nu/\Omega)^2 or (1+\nu/\Omega); this typo propagates into the ratio T_E/T_A.
[General] The text refers to 'the action (34)' in Sec. II, but the action is Eq. (1); Eq. (34) is the scalar-field action in Sec. IV. Also, l is defined as g_1 b^2/2 and later as g_0 b^2/2, which conflicts.
[Section IV, after Eq. (45)] The sentence after Eq. (45) says \Omega \gg A(r_e) instead of \Omega \gg A'(r_e).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Lorentz-violation-dependent transition probability and HBAR entropy are computed from the KR metric and the detector Hamiltonian, not fitted or definitionally assumed.

full rationale

The derivation chain is self-contained given the input KR metric (Eq. 11, taken from [36]) and the standard atom-field interaction Hamiltonian (Eq. 39). The l-dependence enters only through A'(re) (Eq. 30) and re (Eq. 31), which are fixed by the KR metric; no parameter is fitted to the output quantities. The transition probability (Eq. 44) is presented as an evaluation of the integral in Eq. 42, and the HBAR entropy (Eqs. 60-64) is obtained by combining that probability with the Lindblad master equation and the area derivative relation (Eqs. 66-69). Even if Eq. 44 has an algebraic defect, as the skeptic's independent integration suggests, that is a correctness risk rather than a circularity: the claimed result does not reduce to an input by construction. The only self-citation, the author's bumblebee paper [62], is used in the conclusion for qualitative comparison and is not load-bearing for any step in the KR calculation.

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

The central results rest on the KR action and metric inherited from prior literature, the near-horizon Rindler expansion, the ordering of frequencies, and the mirror vacuum; the only genuine free model parameter is l.

free parameters (1)

Lorentz-violating parameter l = not determined; constrained to 0 <= l < 1
Appears in the KR metric, horizon radius, Hawking temperature, transition probability, and HBAR entropy. No independent measurement or derivation fixes its value; it is a free parameter of the model.

assumptions (6)

domain assumption KR gravity action and spontaneous Lorentz violation through the VEV of B_mu_nu
The derivation starts from the action in Eq. (1) and the potential V(x)=lambda x^2/2 with V'=0, leading to b_{\mu\nu}b^{\mu\nu}=-b^2; this is the string inspired model, not independently verified.
domain assumption The KR black hole metric in Eq. (11) is the correct spacetime
The paper imports the solution from [36]; all subsequent formulas for the horizon, temperature, and radiation depend on this metric.
ad hoc to paper Near-horizon first-order Taylor expansion of A(r)
Eq. (26) truncates A(r) at first order in (r-r_e); this is the step that turns the metric into Rindler form and yields the Planck-like factor. Higher-order terms are neglected without error estimates.
ad hoc to paper Frequency ordering Omega >> A'(r_e), nu, k
Introduced after Eq. (43) to evaluate the transition probability integral in closed form; if it fails, the simple exponential expression for P_e is invalid.
domain assumption Boulware vacuum and mirror configuration
The paper adopts the mirror model from [71] so the field starts in a Boulware-like vacuum; transition probabilities are vacuum dependent, so this choice is load-bearing.
standard math Lindblad master equation for the atomic density matrix
The HBAR entropy calculation uses Eq. (52) with steady state solution to relate excitation and absorption rates; this is standard open quantum system formalism.

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Cite this review

Pith. "Pith review of An atom in front of Lorentz violating Kalb-Ramond black hole background." pith.science (2026). https://pith.science/paper/FMQANQO6

@misc{pith2026250601006,
  author       = {Pith},
  title        = {Pith review of: An atom in front of Lorentz violating Kalb-Ramond black hole background},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FMQANQO6}},
  note         = {Machine review of arXiv:2506.01006}
}

read the original abstract

We investigate the role of Lorentz violation in the acceleration radiation produced when an atom falls into a Kalb-Ramond (KR) black hole and observe that the amplitude and an exponential (Planck-like) factor are both shaped by the Lorentz-violating parameter, indicating a breach of the equivalence principle and resembling characteristics observed in bumblebee gravity models. We further investigate how Lorentz violation and conformal symmetry work together to determine the thermodynamic behavior of the system and the implications for the equivalence principle by looking at the transition probabilities of a two-level atomic detector interacting with the black hole. These findings provide new information about the interaction of black hole entropy, symmetry breaking, and possible observational probes of novel physics beyond general relativity. The horizon brightening acceleration radiation (HBAR) entropy in the KR black hole spacetime is also calculated in detail. Although the corrections are very different from those in bumblebee gravity, our study demonstrates that even though Lorentz-violating events alter the entropy, it nevertheless maintains a structural resemblance to the ordinary Bekenstein-Hawking entropy.

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Integrals of motion on extremals of the equation Euler-Lagrange
physics.class-ph 2025-08 unverdicted novelty 4.0 of 10

The paper claims that Wronskian determinants of closed first-order ODE systems serve as integrals of motion on Euler-Lagrange extremals, constructed via the Jacobi equation.

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Works this paper leans on

74 extracted references · 73 canonical work pages · cited by 1 Pith paper

[62]

Rahaman ’ Impact of Lorentz violation on Radiative tr ansition of an atom falling into spherically symmetric blac k hole and related HBAR entropy’ arXiv:2503.23553

A. Rahaman ’ Impact of Lorentz violation on Radiative tr ansition of an atom falling into spherically symmetric blac k hole and related HBAR entropy’ arXiv:2503.23553

arXiv
[1]

Einstein, Sitzungsber Preuss Akad Wiss 844 (1915)

A. Einstein, Sitzungsber Preuss Akad Wiss 844 (1915)

work page 1915
[2]

Einstein, Ann

A. Einstein, Ann. der Physik 49 769 (1916)

work page 1916
[3]

Hawking, Nature 248 30 (1974)

S.W. Hawking, Nature 248 30 (1974)

work page 1974
[4]

Hawking, Commun

S.W. Hawking, Commun. Math. Phys 43 199 (1975)

work page 1975
[5]

Bekenstein, Lett

J.D. Bekenstein, Lett. Nuovo Cimento 4 737 (1972)

work page 1972
[6]

J. D. Bekenstein, Phys. rev. D 7 2333 (1973)

work page 1973
[7]

D. N. Page, Phys. rev. D 13 198 (1976)

work page 1976

Show all 74 references

[8]

D. N. Page, Phys. rev. D 14 3260 (1976)

1976
[9]

D. N. Page, Phys. rev. D 16 2402 (1977)

1977
[10]

W. G. Unruh, Phys. rev. D 14 870 (1976)

1976
[11]

B. S. DeWitt, General relativity: An Einstein Centenar y Survey, eds S. W. Hawking, W. Israel (Cambridge Univ Press (1979), Cambridge, UK)

1979
[12]

W. G. Unruh and R. M. Wald, Phys. rev. D 29 1047 (1984)

1984
[13]

M¨ uller, Phys

R. M¨ uller, Phys. rev. D 56 953 (1997)

1997
[14]

D. A. T. Vanzella and G. E. A. Matsas, Phys. rev. Lett. 87 ( 2001) 151301.enddocument

2001
[15]

H. E. Camblong, A. Chakraborty and C. R. Ord´ o˜ nez, Phys . rev. D 102 085010 (2020)

2020
[16]

Azizi, H

A. Azizi, H. E. Camblong, A. Chakraborty, C. R. Ord´ o˜ nez and M. O. Scully, Phys. rev. D 104 065006 (2021)

2021
[17]

Azizi, H

A. Azizi, H. E. Camblong, A. Chakraborty, C. R. Ord´ o˜ nez and M. O. Scully, Phys. rev. D 104 084086 (2021)

2021
[18]

Azizi, H

A. Azizi, H. E. Camblong, A. Chakraborty, C. R. Ord´ o˜ nez and M. O. Scully, Phys.rev.D104 084085 (2021)

2021
[19]

L. C. B. Crispino, A. Higuchi, G. E. A. Matsas, rev. Mod. P hys. 80 787 (2008)

2008
[20]

M. O. Scully, S. A. Fulling, D. M. Lee, D. N. Page, W. P. Sch leich, A. A. Svidzinsky, Proc. Natl. Acad. Sci. U.S.A. 115 8131 (2018)

2018
[21]

Weiss, Sci

P. Weiss, Sci. News 157 86 (2000)

2000
[22]

T. G. Philbin, et al., Science 319 1367 (2008)

2008
[23]

S. Sen, R. Mandal and S. Gangopadhyay, Phys.rev.D 105 08 5007 (2022)

2022
[24]

Chakraborty, B

K. Chakraborty, B. R. Majhi Phys. Rev. D 100, 045004 (201 9)
[25]

P. K. Kumawat, S. Barman, B. R. Majhi JCAP 02 046 (2025)

2025
[26]

Castro, A

A. Castro, A. Maloney and A. Strominger, Phys. rev. D 82 0 24008 (2010)

2010
[27]

Agullo, J

I. Agullo, J. Navarro-Salas, G. J. Olmo, L. Parker, Phys . rev. Lett. 105 211305 (2010)

2010
[28]

Rovelli, Living

C. Rovelli, Living. rev. relativ. 1 1 (1998)

1998
[29]

Carlip, rep

S. Carlip, rep. Prog. Phys. 64 885 (2001)

2001
[30]

Amati, M

D. Amati, M. Ciafaloni and G. Veneziano, Phys. Lett. B 21 6 41 (1989)

1989
[31]

Konishi, G

K. Konishi, G. Paﬀuti and P. Provero, Phys. Lett. B 234 27 6 (1990)

1990
[32]

M. Kalb, P. Ramond, Phys. rev. D 9 2273 (1974)

1974
[33]

Cremmer, J

E. Cremmer, J. Scherk, Nucl. Phys. B72 (1974)

1974
[34]

Ellis, N

J. Ellis, N. E. Mavromatos and D. V. Nanopoulos, Phys. Le tt. B 267 465 (1991)

1991
[35]

Bluhm, Lect

R. Bluhm, Lect. Notes Phys. 702 191 (2006)

2006
[36]

K. Yang, Y. Z. Chen, Z.Q .Duan and J.Y. Zhao, Phys. rev. D 1 08 124004 (2023)

2023
[37]

V. A. Kostelecky S. Samuel, Phys. rev. D 39 683, (1989)

1989
[38]

Jackiw and S.-Y

R. Jackiw and S.-Y. Pi, Phys. rev. D 68 104012 (2003)

2003
[39]

N. E. Mavromatos, PoS QG-PH, 027 (2007)

2007
[40]

Kostelecky, S

V.A. Kostelecky, S. Samuel, Phys. rev. D 40, 1886 (1989)

1989
[41]

Casana, A

R. Casana, A. Cavalcante, F.P. Poulis, E.B. Santos, Phy s. rev. D 97, 104001 (2018)

2018
[42]

W. Liu, X. Fang, J. Jing, J. Wang,, Eur. Phys. J. C 83, 83 (2 023)
[43]

S. K. Jha, A. Rahaman, Eur. Phys. J. C 81, 345(2021)

2021
[44]

R. V. Maluf, J. C. S. Neves, Phys. rev. D 103, 044002 (2021 )

2021
[45]

M. D. Seifert, Phys. rev. D 81, 065010 (2010)

2010
[46]

C. Ding, X. Chen, and X. Fu, Nucl. Phys. B 975, 115688 (202 2)
[47]

Oliveira, D.M

R. Oliveira, D.M. Dantas, C.A.S. Almeida,EPL 135, 1000 3 (2021)

2021
[48]

Kosteleck, R

Alan V. Kosteleck, R. Lehnert, Physical review D. 63 065 008 (2001)

2001
[49]

Kosteleck, Physical review D

Alan V. Kosteleck, Physical review D. 69 (10): 105009 (2 004)
[50]

Q. G. Bailey, Alan V. Kostelecky Phys. rev. D 74, 045001 ( 2006)

2006
[51]

Bluhm, N Gagne, R

R. Bluhm, N Gagne, R. Potting, A. Vrublevskis, Physical review D. 77 125007 ((2008))

2008
[52]

Koivisto and D

T. Koivisto and D. F. Mota, JCAP 0808 021 (2008)

2008
[53]

Mukhopadhyay, S

S. Mukhopadhyay, S. Chakraborty, Eur. Phys. J. C, 79 872 ( 2019)

2019
[54]

Dey and S

A. Dey and S. Sarkar, N. Banerjee, Phys. rev. D 94, 104068 (2016)

2016
[55]

Singleton, S

D. Singleton, S. Wilburn, Phys.rev.Lett. 108 (2012) 04 9002

2012
[56]

Singleton and S

D. Singleton and S. Wilburn, Phys. rev. Lett. 107 081102 (2011)

2011
[57]

Chatterjee, S

R. Chatterjee, S. Gangopadhyay, A. S. Majumdar Phys. re v. D 104, 124001 (2021)

2021
[58]

Lindblad, Commun

G. Lindblad, Commun. Math. Phys. 119 48 (1976)

1976
[59]

D. G. Boulware, Phys. Rev. D 11 1404 (1975). 12

1975
[60]

Altschul, Q

B. Altschul, Q. G.Bailey and V. A. Kostelecky, Phys. rev . D 81 (2010), 065028

2010
[61]

L. A. Lessa, J. E. G.Silva, R. V.Maluf and C. A. S. Almeida ,, Eur. Phys. J. C 80 no.4, 335 (2020)

2020
[63]

reuter, Phys

M. reuter, Phys. rev. D 57 971 (1998)

1998
[64]

Wetterich, Phys, Lett

C. Wetterich, Phys, Lett. B 301 90 (1993)

1993
[65]

reuter and C

M. reuter and C. Wetterich, Nucl. Phys. B 417 181 (1994)

1994
[66]

Saueressig and M

F. Saueressig and M. reuter, ” Quantum Gravity and the” Functional renormalization Group: The Road towards Asympt otic Safety (Cambridge monographs on mathematical physics)”, C ambridge University Press (2019)

2019
[67]

Bonanno and M

A. Bonanno and M. reuter, Phys. rev. D 62 043008 (2000)

2000
[68]

Rohrlich, Ann

F. Rohrlich, Ann. Phys. 22 169 (1963)

1963
[69]

Pauri and M

M. Pauri and M. Vallisneri, Foun. Phys. 29 1499 (1999)

1999
[70]

Singleton and S

D. Singleton and S. Wilburn, Int. J. Mod. Phys. D 25 16440 09 (2016)

2016
[71]

A. A. Svidzinsky, S. J. Ben-Benjamin, S. A. Fulling and D . N. Page, Phys. rev. Lett 121 071301 (2018)

2018
[72]

S. A. Fulling and J. H. Wilson, Phys. Scr. 94 014004 (2019 )

2019
[73]

Chatterjee, S

R. Chatterjee, S. Gangopadhyay and A. S. Majumdar, Phys . rev. D 104 124001 (2021)

2021
[74]

R. K. Kaul and P. Majumdar, Phys. rev. Lett. 84 5255 (2000 )

2000

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [62]

Rahaman ’ Impact of Lorentz violation on Radiative tr ansition of an atom falling into spherically symmetric blac k hole and related HBAR entropy’ arXiv:2503.23553

A. Rahaman ’ Impact of Lorentz violation on Radiative tr ansition of an atom falling into spherically symmetric blac k hole and related HBAR entropy’ arXiv:2503.23553

arXiv

[2] [1]

Einstein, Sitzungsber Preuss Akad Wiss 844 (1915)

A. Einstein, Sitzungsber Preuss Akad Wiss 844 (1915)

work page 1915

[3] [2]

Einstein, Ann

A. Einstein, Ann. der Physik 49 769 (1916)

work page 1916

[4] [3]

Hawking, Nature 248 30 (1974)

S.W. Hawking, Nature 248 30 (1974)

work page 1974

[5] [4]

Hawking, Commun

S.W. Hawking, Commun. Math. Phys 43 199 (1975)

work page 1975

[6] [5]

Bekenstein, Lett

J.D. Bekenstein, Lett. Nuovo Cimento 4 737 (1972)

work page 1972

[7] [6]

J. D. Bekenstein, Phys. rev. D 7 2333 (1973)

work page 1973

[8] [7]

D. N. Page, Phys. rev. D 13 198 (1976)

work page 1976