pith. machine review for the scientific record. sign in

arxiv: 2604.03518 · v1 · submitted 2026-04-03 · 🌀 gr-qc

Recognition: no theorem link

Dynamical Black Hole Thermodynamics in Modified Gravity

Nikko John Leo S. Lobos , Emmanuel T. Rodulfo
Authors on Pith no claims yet

Pith reviewed 2026-05-13 17:46 UTC · model grok-4.3

classification 🌀 gr-qc
keywords dynamicalblackgravityholeinformationmodifiednon-thermalparadox
0
0 comments X

The pith

In modified gravity, dynamical Schwarzschild black holes under scalar waves exhibit non-thermal particle creation while preserving the generalized second law and forming stable zero-temperature remnants at the extremal bound.

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

The authors analyze a black hole in modified gravity theory, which includes an extra vector field and scalar degrees of freedom beyond standard general relativity. They focus on the apparent horizon that changes with time due to an incoming scalar gravitational wave in breathing mode. This time dependence alters the surface gravity and temperature in a way that breaks the usual slow, adiabatic approximation used in black hole thermodynamics. As a result, particles are created in a non-thermal spectrum rather than the familiar Hawking radiation. To resolve an apparent violation of the second law of thermodynamics, they separate quick reversible changes in the horizon geometry from slower irreversible entropy production, relying on the Raychaudhuri equation that tracks how light rays converge or diverge. On short timescales, the non-thermal emission provides a channel for information to leave the black hole. On long timescales, the repulsive vector charge stops the black hole from evaporating completely once its mass approaches the charge value, leaving a cold, stable remnant. These effects are presented as testable signatures for future gravitational-wave detectors.

Core claim

The Generalized Second Law remains preserved by decoupling first-order reversible kinematic-horizon fluctuations from second-order irreversible entropy growth using the Raychaudhuri equation, while the massive vector field halts evaporation as mass approaches the extremal bound M_G to Q_G yielding a stable zero-temperature remnant.

Load-bearing premise

The scalar gravitational wave breathing mode can be imposed on the Schwarzschild background in MOG while treating the evolution as quasi-adiabatic without significant backreaction from the created particles or the vector field altering the metric at leading order.

Figures

Figures reproduced from arXiv: 2604.03518 by Emmanuel T. Rodulfo, Nikko John Leo S. Lobos.

Figure 1
Figure 1. Figure 1: FIG. 1. Entropy production rates for a dynamically perturbed [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The MOG resolution to the black hole information paradox. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

We study the dynamical and thermodynamic evolution of a Schwarzschild black hole in Modified Gravity (MOG) under a scalar gravitational wave breathing mode. The time-dependent apparent horizon reveals that both the scalar strain velocity and the repulsive vector charge modulate the effective surface gravity and the instantaneous dynamical temperature in a quasi-adiabatic way. As a result, this regime breaks the semiclassical adiabatic approximation and triggers explicit non-thermal particle creation. We resolve a thermodynamic paradox by decoupling first-order reversible kinematic-horizon fluctuations from second-order irreversible entropy growth, using the Raychaudhuri equation. Consequently, the Generalized Second Law remains preserved. We apply these results to address the black hole information paradox across two timescales. Short-term non-thermal emission opens a dynamical channel for the escape of correlated geometric information. On long timescales, the massive vector field halts evaporation as mass approaches the extremal bound, $M_G \to Q_G$. This yields a stable, zero-temperature remnant. These signals provide a framework for probing scalar-tensor-vector modifications to general relativity with next-generation gravitational-wave observatories

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.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard Raychaudhuri equation extended to MOG, the definition of the apparent horizon in dynamical spacetimes, and the MOG vector charge as a fixed parameter that sets the extremal limit. No new entities are postulated beyond the existing MOG fields.

free parameters (1)
  • vector charge Q_G
    Sets the extremal bound where evaporation halts; treated as an input parameter of the MOG theory rather than derived from the wave dynamics.
axioms (2)
  • domain assumption Raychaudhuri equation governs null geodesic congruence in MOG
    Invoked to separate first-order reversible horizon fluctuations from second-order irreversible entropy production.
  • ad hoc to paper Quasi-adiabatic evolution under scalar breathing mode
    Assumed to allow modulation of surface gravity without dominant backreaction.

pith-pipeline@v0.9.0 · 5487 in / 1577 out tokens · 69887 ms · 2026-05-13T17:46:09.600591+00:00 · methodology

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

37 extracted references · 37 canonical work pages · 2 internal anchors

  1. [1]

    B. P. Abbottet al.(LIGO Scientific, Virgo), Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett.116, 061102 (2016)

    work page 2016

  2. [2]

    C. M. Will, The Confrontation between General Rela- tivity and Experiment, Living Rev. Rel.17, 4 (2014), arXiv:1403.7377 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  3. [4]

    J. W. Moffat and S. Rahvar, The MOG weak field approxi- mation and observational test of galaxy rotation curves, Eur. Phys. J. C73, 2665 (2013), arXiv:1306.6383 [astro-ph.GA]

    work page arXiv 2013

  4. [5]

    J. W. Moffat, Modified Gravity Black Holes and their Observable Shadows, Eur. Phys. J. C75, 130 (2015), arXiv:1502.01677 [gr-qc]

    work page arXiv 2015

  5. [6]

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

    K. 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]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  6. [7]

    J. W. Moffat, Black Holes in Modified Gravity (MOG), Eur. Phys. J. C75, 175 (2015), arXiv:1412.5424 [gr-qc]

    work page arXiv 2015

  7. [8]

    D. M. Eardley, D. L. Lee, and A. P. Lightman, Gravitational- wave observations as a tool for testing relativistic gravity, Phys. Rev. D8, 3308 (1973)

    work page 1973

  8. [9]

    B. P. Abbottet al.(LIGO Scientific, Virgo), GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett.119, 141101 (2017), arXiv:1709.09660 [gr-qc]

    work page Pith review arXiv 2017

  9. [10]

    J. D. Bekenstein, Black holes and entropy, Phys. Rev. D7, 2333 (1973)

    work page 1973

  10. [11]

    S. W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys.43, 199 (1975), [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    work page 1975

  11. [12]

    S. A. Hayward, General laws of black hole dynamics, Phys. Rev. D49, 6467 (1994), arXiv:gr-qc/9303006

    work page arXiv 1994

  12. [13]

    Isolated and dynamical horizons and their applications

    A. Ashtekar and B. Krishnan, Isolated and dynamical hori- zons and their applications, Living Rev. Rel.7, 10 (2004), arXiv:gr-qc/0407042

    work page Pith review arXiv 2004

  13. [14]

    J. R. Mureika, J. W. Moffat, and M. Faizal, Black Hole Thermodynamics in MOdified Gravity (MOG), Phys. Lett. B757, 528 (2016), arXiv:1504.08226 [gr-qc]

    work page arXiv 2016

  14. [15]

    J. D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D9, 3292 (1974)

    work page 1974

  15. [16]

    A. C. Wall, A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices, Phys. Rev. D 85, 104049 (2012)

    work page 2012

  16. [17]

    S. W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D14, 2460 (1976)

    work page 1976

  17. [18]

    N. J. L. S. Lobos and E. T. Rodulfo, Breathing black hole shadows in modified gravity (mog), arXiv preprint arXiv:2602.21432 (2026)

    work page arXiv 2026

  18. [19]

    R. C. Pantig, Shadow ringing of black holes from photon sphere quasinormal modes, Annals Phys.488, 170383 (2026), arXiv:2509.24479 [hep-th]

    work page arXiv 2026

  19. [20]

    R. M. Wald,General Relativity(Chicago Univ. Pr., Chicago, USA, 1984)

    work page 1984

  20. [21]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation 7 (W. H. Freeman, San Francisco, 1973)

    work page 1973

  21. [22]

    G. D. Birkhoff,Relativity and Modern Physics(Harvard University Press, 1923)

    work page 1923

  22. [23]

    Roshan, Test of Birkhoff’s theorem in Scalar-Tensor- Vector Gravity, Phys

    M. Roshan, Test of Birkhoff’s theorem in Scalar-Tensor- Vector Gravity, Phys. Rev. D87, 044005 (2013)

    work page 2013

  23. [24]

    J. W. Moffat, Scalar-tensor-vector gravity theory, JCAP03 (04), 004, arXiv:gr-qc/0506021

    work page arXiv

  24. [25]

    S. W. Hawking, Gravitational radiation from colliding black holes, Phys. Rev. Lett.26, 1344 (1971)

    work page 1971

  25. [26]

    A. B. Nielsen and M. Visser, Production and decay of appar- ent horizons, Class. Quant. Grav.23, 4637 (2006), arXiv:gr- qc/0510083

    work page arXiv 2006

  26. [27]

    N. D. Birrell and P. C. W. Davies,Quantum Fields in Curved Space(Cambridge University Press, 1984)

    work page 1984

  27. [28]

    Parker, Particle creation in expanding universes, Phys

    L. Parker, Particle creation in expanding universes, Phys. Rev. Lett.21, 562 (1968)

    work page 1968

  28. [29]

    D. N. Page, Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole, Phys. Rev. D13, 198 (1976)

    work page 1976

  29. [30]

    S. W. Hawking, Black Holes and Thermodynamics, Phys. Rev. D13, 191 (1976)

    work page 1976

  30. [31]

    S. D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav.26, 224001 (2009)

    work page 2009

  31. [32]

    P. Chen, Y. C. Ong, and D.-h. Yeom, Black Hole Remnants and the Information Loss Paradox, Phys. Rept.603, 1 (2015)

    work page 2015

  32. [33]

    R. J. Adler, P. Chen, and D. I. Santiago, The Generalized uncertainty principle and black hole remnants, Gen. Rel. Grav.33, 2101 (2001), arXiv:gr-qc/0106080

    work page arXiv 2001

  33. [34]

    G. T. Moore, Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity, J. Math. Phys. 11, 2679 (1970)

    work page 1970

  34. [35]

    V. V. Dodonov, Current status of the dynamical Casimir effect, Phys. Scripta82, 038105 (2010)

    work page 2010

  35. [36]

    K. D. Kokkotas and B. G. Schmidt, Quasinormal modes of stars and black holes, Living Rev. Rel.2, 2 (1999)

    work page 1999

  36. [37]

    M. K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett.85, 5042 (2000)

    work page 2000

  37. [38]

    D. N. Page, Information in black hole radiation, Phys. Rev. Lett.71, 3743 (1993)

    work page 1993