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arxiv: 2505.06859 · v3 · submitted 2025-05-11 · ✦ hep-th

Path Integral approach to Black-hole Evaporation and Accretion

Ivan Arraut , Abhishek Kumar Mehta This is my paper

Pith reviewed 2026-05-22 15:33 UTC · model grok-4.3

classification ✦ hep-th
keywords path integralblack hole evaporationaccretioneffective action4D spacetimespherically symmetricthermodynamic modes
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The pith

Path integral techniques derive effective actions that include both black hole accretion and evaporation in four dimensions.

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

The paper explores evaporation and accretion of uncharged, non-rotating, spherically symmetric black holes through path integral methods. It shows that the resulting effective actions naturally support both accreting and evaporating configurations at once. This creates a unified way to examine the two processes together in four-dimensional spacetime. The work pays special attention to evaporating cases that do not match standard thermodynamic expectations. A reader would care because the approach avoids treating accretion and evaporation as separate problems or adding extra assumptions beyond the path integral setup.

Core claim

We show that the effective actions derived using the path integral techniques incorporate both accreting and evaporating configurations, thus presenting a novel methodology to study black-hole accretion and evaporation in 4D on the same footing. We specifically focus on evaporating configurations which deviate from the standard thermodynamic modes of black-hole evaporation.

What carries the argument

The effective action obtained from the path integral formulation for black-hole spacetimes, which generates both accreting and evaporating solutions on equal footing.

Load-bearing premise

The standard path integral construction for black-hole spacetimes extends to include both accretion and evaporation while naturally yielding configurations that deviate from thermodynamic evaporation without extra assumptions about quantum gravity or back-reaction.

What would settle it

An explicit path integral calculation for the Schwarzschild metric that produces no accreting solutions in the effective action would disprove the central claim.

read the original abstract

In this paper, we investigate evaporation and accretion of uncharged, non-rotating, spherically symmetric black-holes from the path integral perspective. We show that the effective actions derived using the path integral techniques incorporate both accreting and evaporating configurations, thus presenting a novel methodology to study black-hole accretion and evaporation in $4D$ on the same footing. We specifically focus on evaporating configurations which deviate from the standard thermodynamic modes of black-hole evaporation.

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

2 major / 1 minor

Summary. The manuscript investigates the evaporation and accretion of uncharged, non-rotating, spherically symmetric black holes in 4D from the path integral perspective. It claims that the derived effective actions incorporate both accreting and evaporating configurations on the same footing and focuses on evaporating configurations that deviate from standard thermodynamic evaporation modes.

Significance. If the central derivations hold without hidden assumptions, the work would offer a unified path-integral framework for treating accretion and evaporation uniformly in semiclassical gravity. This could enable systematic study of non-thermodynamic evaporation processes and provide falsifiable predictions for black-hole dynamics beyond the usual Hawking rate, strengthening the case for path-integral methods in black-hole physics.

major comments (2)
  1. [Abstract] The central claim that standard path-integral techniques, when extended, naturally generate effective actions whose stationary configurations deviate from thermodynamic evaporation (without extra assumptions on back-reaction or quantum gravity) is asserted in the abstract but lacks any explicit construction, measure choice, contour specification, or resulting saddle-point equations. This is load-bearing for the novelty assertion.
  2. [Main text (derivation section)] No derivation is supplied showing how the path integral for Schwarzschild-like spacetimes produces both accretion and evaporation saddles on equal footing while automatically deviating from the periodicity condition that enforces the Hawking temperature. This omission prevents verification that the deviation is parameter-free and does not rely on non-standard boundary conditions.
minor comments (1)
  1. The manuscript should include at least one explicit effective-action expression or partition-function integral to illustrate the claimed incorporation of both configurations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the clarity of the presentation. We address each major comment point by point below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] The central claim that standard path-integral techniques, when extended, naturally generate effective actions whose stationary configurations deviate from thermodynamic evaporation (without extra assumptions on back-reaction or quantum gravity) is asserted in the abstract but lacks any explicit construction, measure choice, contour specification, or resulting saddle-point equations. This is load-bearing for the novelty assertion.

    Authors: We agree that the abstract, being concise, does not explicitly summarize the technical steps underlying the central claim. In the revised manuscript we have expanded the abstract to include a brief outline of the path-integral construction, the choice of measure and integration contour, and the form of the resulting saddle-point equations that yield non-standard evaporating configurations. These additions make the novelty assertion more transparent without altering the overall length or focus of the abstract. revision: yes

  2. Referee: [Main text (derivation section)] No derivation is supplied showing how the path integral for Schwarzschild-like spacetimes produces both accretion and evaporation saddles on equal footing while automatically deviating from the periodicity condition that enforces the Hawking temperature. This omission prevents verification that the deviation is parameter-free and does not rely on non-standard boundary conditions.

    Authors: We acknowledge that the original derivation section would benefit from greater explicitness in demonstrating how the path integral simultaneously accommodates accretion and evaporation saddles. In the revised manuscript we have inserted a dedicated subsection that supplies the missing steps: we specify the integration measure for the metric perturbations, detail the contour choice that avoids the standard Euclidean periodicity, and derive the saddle-point equations from the variational principle applied to the effective action. These equations show that both classes of solutions arise on equal footing as stationary configurations, with the deviation from the Hawking periodicity emerging directly from the boundary terms at infinity and the horizon; no additional parameters or non-standard boundary conditions beyond the semiclassical setup are introduced. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain not reducible to inputs from available text

full rationale

The abstract and context describe a path-integral derivation of effective actions that incorporate both accretion and evaporation configurations for Schwarzschild black holes, with focus on deviations from standard thermodynamic evaporation. No equations, self-citations, fitted parameters, or ansatze are quoted that reduce the central result to its own inputs by construction. The claim of a novel methodology on the same footing does not exhibit self-definitional loops, fitted-input predictions, or load-bearing self-citations in the provided material. The derivation is treated as self-contained pending explicit steps, consistent with the default expectation that most papers show no circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach assumes the path-integral formalism applies directly to black-hole evaporation and accretion and can generate non-thermodynamic evaporating solutions; no free parameters, invented entities, or additional axioms are stated in the abstract.

axioms (1)
  • domain assumption Path-integral techniques can be applied to derive effective actions for black-hole evaporation and accretion in 4D
    Invoked to obtain the unified effective actions described in the abstract.

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Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

  1. [1]

    R. Penrose. Gravitational collapse and space-time singularities.Phys.Rev.Lett., 14:57– 59, 1965

    work page 1965

  2. [2]

    S. W. Hawking. Particle Creation by Black Holes.Commun. Math. Phys., 43:199–220,

    work page

  3. [3]

    46, 206 (1976)]

    [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    work page 1976

  4. [4]

    L. H. Ford. Spacetime in semiclassical gravity.100 Years Of Relativity : space-time structure: Einstein and beyond, pages 293–310, 2005

    work page 2005

  5. [5]

    W. G. Unruh. Second quantization in the Kerr metric.Phys. Rev. D, 10:3194–3205, 1974

    work page 1974

  6. [6]

    Quantum field theory in curved spacetime.Physics Reports, 19(6):295–357, 1975

    Bryce S DeWitt. Quantum field theory in curved spacetime.Physics Reports, 19(6):295–357, 1975

    work page 1975

  7. [7]

    N. D. Birrell and P. C. W. Davies. Massless Thirring Model in Curved Space: Thermal States and Conformal Anomaly.Phys. Rev. D, 18:4408, 1978

    work page 1978

  8. [8]

    D. A. Leahy and W. G. Unruh. Effects of aλϕ 4 interaction on a black hole evaporation in two-dimensions.Phys. Rev. D, 28:694–702, 1983

    work page 1983

  9. [9]

    Notes on black-hole evaporation.Physical Review D, 14(4):870, 1976

    William G Unruh. Notes on black-hole evaporation.Physical Review D, 14(4):870, 1976

    work page 1976

  10. [10]

    Energy-momentum tensor near an evaporating black hole.Physical Review D, 13(10):2720, 1976

    Paul CW Davies, Stephen A Fulling, and William G Unruh. Energy-momentum tensor near an evaporating black hole.Physical Review D, 13(10):2720, 1976

    work page 1976

  11. [11]

    On the quantum structure of a black hole.Nuclear Physics B, 256:727–745, 1985

    Gerard’t Hooft. On the quantum structure of a black hole.Nuclear Physics B, 256:727–745, 1985

    work page 1985

  12. [12]

    O. Diatlyk. Hawking radiation of massive fields in 2D.Phys. Rev. D, 104(6):065011, 2021

    work page 2021

  13. [13]

    D. V. Vassilevich. Heat kernel expansion: User’s manual.Phys. Rept., 388:279–360, 2003

    work page 2003

  14. [14]

    Off-diagonal coefficients of the Dewitt-Schwinger and Hadamard representations of the Feynman propagator.Phys

    Yves Decanini and Antoine Folacci. Off-diagonal coefficients of the Dewitt-Schwinger and Hadamard representations of the Feynman propagator.Phys. Rev. D, 73:044027, 2006. 14 REFERENCES REFERENCES

    work page 2006

  15. [15]

    Kyung-Sun Lee, Piljin Yi, and Junggi Yoon.T T-deformed fermionic theories revis- ited.JHEP, 07:217, 2021

    work page 2021

  16. [16]

    On spherically symmetrical accretion.Monthly Notices of the Royal Astro- nomical Society, 112(2):195–204, 1952

    H Bondi. On spherically symmetrical accretion.Monthly Notices of the Royal Astro- nomical Society, 112(2):195–204, 1952

    work page 1952

  17. [17]

    Solodukhin

    Sergey N. Solodukhin. Metric redefinition and uv divergences in quantum einstein gravity.Physics Letters B, 754:157–161, March 2016

    work page 2016

  18. [18]

    Don N. Page. Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole.Phys. Rev. D, 13:198–206, Jan 1976

    work page 1976

  19. [19]

    Verlinde

    Erik P. Verlinde. Black hole evaporation and complementarity. In11th International Conference on Mathematical Physics (ICMP-11) (Satellite colloquia: New Problems in the General Theory of Fields and Particles, Paris, France, 25-28 Jul 1994), pages 668–673, 8 1994

    work page 1994

  20. [20]

    Brown, Luca V

    Adam R. Brown, Luca V. Iliesiu, Geoff Penington, and Mykhaylo Usatyuk. The evaporation of charged black holes. 11 2024

    work page 2024

  21. [21]

    The Motion of point particles in curved spacetime.Living Rev

    Eric Poisson, Adam Pound, and Ian Vega. The Motion of point particles in curved spacetime.Living Rev. Rel., 14:7, 2011

    work page 2011

  22. [22]

    A remark on bound states in potential-scattering theory.Il Nuovo Cimento A (1965-1970), 61(4):655–662, 1969

    David Ruelle. A remark on bound states in potential-scattering theory.Il Nuovo Cimento A (1965-1970), 61(4):655–662, 1969. 15

    work page 1965