Simpson-Visser-AdS Black Holes: Thermodynamics and Binary Merger

Ankur Srivastav; Neeraj Kumar; Phongpichit Channuie

arxiv: 2511.21424 · v3 · submitted 2025-11-26 · 🌀 gr-qc

Simpson-Visser-AdS Black Holes: Thermodynamics and Binary Merger

Neeraj Kumar , Ankur Srivastav , Phongpichit Channuie This is my paper

Pith reviewed 2026-05-17 05:09 UTC · model grok-4.3

classification 🌀 gr-qc

keywords black hole thermodynamicsSimpson-Visser regularizationAdS black holesphase transitionsbinary mergersregular black holesentropy

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The pith

Simpson-Visser regularization of AdS black holes yields an entropy that satisfies the first law and produces phase transitions plus merger mass bounds that vary non-trivially with the regularization parameter.

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

The paper regularizes Anti-de Sitter black holes using the Simpson-Visser scheme and checks that the first law of thermodynamics still holds for the resulting geometry. From this it derives a consistent entropy expression. Free-energy calculations then show that the phase structure changes in a non-trivial way as the regularization parameter is varied. The work also applies the second law to the merger of two equal-mass regular black holes and tracks how the allowed range of final masses shifts with the same parameter, first widening and then narrowing sharply before recovering the ordinary AdS case at vanishing parameter.

Core claim

The central claim is that SV-regularized AdS black holes admit a first law with a well-defined entropy, exhibit phase transitions whose character depends on the SV regularization parameter, and produce post-merger mass constraints that increase initially and then decrease sharply as the parameter grows, all while reducing to standard AdS black-hole thermodynamics when the parameter is set to zero.

What carries the argument

The Simpson-Visser regularization parameter inserted into the AdS black-hole metric, which deforms the geometry and thereby modifies the thermodynamic potentials and the constraints derived from the second law during equal-mass mergers.

If this is right

Phase-transition temperatures and critical points become explicit functions of the SV parameter rather than fixed constants.
The allowed interval for post-merger black-hole mass first expands and later contracts with rising SV parameter.
Entropy and free-energy expressions reduce exactly to the standard AdS results when the regularization parameter vanishes.
The second-law constraint on merger outcomes supplies a parameter-dependent upper bound on the final mass.

Where Pith is reading between the lines

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

If the SV-regularized geometry can be embedded in a consistent quantum theory, the parameter might serve as a tunable regulator that preserves thermodynamic laws while removing the central singularity.
The non-monotonic behavior of merger bounds suggests that analogue-gravity experiments or numerical relativity runs could search for a similar peak-and-decline pattern when a regularization scale is introduced.
The same regularization technique could be applied to other asymptotically AdS solutions to test whether the observed phase-transition dependence is generic.

Load-bearing premise

The first and second laws of black hole thermodynamics remain valid in their usual form for the SV-regularized AdS geometry.

What would settle it

A direct computation showing that the derived entropy fails to satisfy the first law differential for the modified metric, or a merger simulation in which the final-mass bounds do not display the reported initial rise followed by a sharp drop as the regularization parameter increases.

Figures

Figures reproduced from arXiv: 2511.21424 by Ankur Srivastav, Neeraj Kumar, Phongpichit Channuie.

**Figure 1.** Figure 1: Hawking temperature vs horizon radius for SV-regular AdS black holes for a = (0, 0.1, 0.2, 0.3) as we set l = 1. black holes, there is a local maxima and a minima and there is an extremal black hole limit for the SV-AdS regular black holes. Since there is a black hole for all values of temperature, there is no stable thermal AdS phase, hence, there is no HawkingPage phase transition [16]. From the plot g… view at source ↗

**Figure 2.** Figure 2: Free energy vs Hawking temperature for SV-AdS regular black holes for a = (0, 0.1, 0.2, 0.3) as we set l = 1. This expression matches with the free energy of a Schwarzschild AdS black hole [16]. We plot the free energy for the SV-AdS regular black holes, given by eq.(11), against Hawking temperature, in Fig.(2), for different values of the SVregularization parameter, a. Dashed plot represents the standar… view at source ↗

**Figure 5.** Figure 5: Final Mass vs SV-Regularization Parameter a as we set l = ∞, Mi = 1. increases too. This range, considered in the analysis, corresponds to the initial mass value Mi and it remains valid in the post merger scenario as well (that is, the solution is still a SV-AdS regular black hole post merger). Now, we shall analyse the case of SV- regularized black hole merger in asymptotically flat spacetime. Merger C… view at source ↗

**Figure 3.** Figure 3: Final Mass vs SV-Regularization Parameter a as we set l = 1 and Mi = 1. the final mass post merger initially increases as we increase the value of a and then starts decreasing after a certain value, indicated by a dashed line. Thus, the bounds on the final mass change nontrivially with respect to SV-regularization parameter, a. The bound corresponding to the standard Schwarzschild AdS black hole is deno… view at source ↗

**Figure 4.** Figure 4: Final Mass vs SV-Regularization Parameter a as we set l = 1 and Mi = 1, 2, 3. 0.5 1.0 1.5 2.0 1.0 1.1 1.2 1 1.4 1.5 Regularization Parameter a Final Mass Mf Mi = 1 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: Final Mass vs SV-Regularization Parameter a as we set l = ∞ and Mi = 1, 2, 3. However, these singularities also predict the demise of general relativity as a complete theory of gravity. SV-regularization scheme is a bottom-up approach which provides a way to circumvent central black hole singularity. The geometry obtained as such is free from singularities and its impacts are visible in classical and ther… view at source ↗

read the original abstract

In this article, we performed Simpson-Visser (SV)-regularization scheme to Anti-de Sitter (AdS) black holes and then studied thermal properties of the resulting spacetime geometry. We considered the validity of the first law of black hole thermodynamics in this case and derived an entropy formula consistent with this new regular geometry. Next, we carried out the free energy analysis and studied the phase structure of these black holes. We discovered non-trivial phase transition properties dependent on the SV-regularization parameter. We also considered the validity of the second law of black hole thermodynamics and analyzed a merger scenario of two equal mass SV-regular black holes. In particular, we investigated the impact of the SV-regularization parameter on the constraints on post-merger black hole mass. Intrestingly, we found that the bounds initially increase and then fall sharply with increasing the SV-regularization parameter. All results are compared with standard black holes for vanishing SV-regularization parameter.

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.

Desk Editor's Note private letter to a colleague

SV-regularized AdS black holes show parameter-dependent phases and non-monotonic merger bounds, but first-law consistency needs explicit checks.

read the letter

The main takeaway here is that regularizing AdS black holes with the Simpson-Visser scheme produces phase transitions that depend on the regularization parameter and merger mass bounds that first rise then drop sharply as the parameter increases. These are the concrete new results the paper reports. The work does a few things right. It starts from the regularized metric, checks that the first law holds, and extracts an entropy that matches. Then it moves to the free energy to map out the phase structure. For the merger part, it applies the second law to two equal-mass black holes and derives bounds on the final mass, showing how the SV parameter affects those bounds. The direct comparison to the vanishing-parameter limit is clear and helpful. Where it could be softer is the explicit verification of thermodynamic consistency. The stress-test note is on point: just asserting that the entropy satisfies the first law is not enough if the paper skips the step of showing that the integral of dM/T recovers the area law or the appropriate Wald entropy for finite regularization. If that check is missing or only done in the limit, the phase analysis and the merger constraints lose some of their foundation. The free parameter is introduced by hand, which is standard for these models, but it means all the interesting behaviors are parametric rather than predicted from first principles. This paper is for specialists in black hole thermodynamics who are already following regularization techniques like Simpson-Visser. A reader who wants to see how such modifications play out in AdS and in dynamical scenarios like mergers will get something out of it. The calculations look standard and the claims are specific, so it is worth a serious referee's time even if the thermodynamic base needs tightening. I would send it to peer review. The referee can request the detailed entropy derivation and comment on whether the non-monotonic behavior has a clear physical interpretation. It is not a big leap, but it is a clean extension that adds to the literature on regular AdS black holes.

Referee Report

2 major / 2 minor

Summary. The paper applies the Simpson-Visser regularization to AdS black holes, asserts that the first law remains valid and derives a consistent entropy, performs free-energy analysis to identify non-trivial phase transitions that depend on the SV-regularization parameter, and examines binary equal-mass mergers under the second law, reporting that post-merger mass bounds first increase and then decrease sharply as the regularization parameter grows, with all results compared to the a=0 Schwarzschild-AdS limit.

Significance. If the thermodynamic consistency can be established, the work supplies a concrete regularized AdS geometry whose phase structure and merger constraints exhibit non-monotonic dependence on the regulator; this could serve as a useful test-bed for extended-phase-space thermodynamics and for second-law bounds in modified spacetimes.

major comments (2)

[§3] §3 (Thermodynamics and entropy derivation): the manuscript states that the first law dM = T dS holds and yields a consistent entropy, yet supplies neither an explicit integration of dM/T for finite SV parameter a nor a Wald-Noether-charge calculation that accounts for the effective stress-energy introduced by the regularization; without this verification the reported phase transitions and merger bounds rest on an unconfirmed identity.
[§4] §4 (Free-energy analysis): the non-trivial phase-transition properties are claimed to depend on the SV parameter, but the absence of an explicitly verified entropy prevents confirmation that the Gibbs free energy G = M − TS is correctly normalized and that the reported swallow-tail behavior is not an artifact of an assumed rather than derived S.

minor comments (2)

[Abstract] Abstract: the word 'Intrestingly' is misspelled.
[§2] Notation: the precise form of the regularized metric function f(r) (e.g., whether the AdS term is −r²/l² or modified) should be written explicitly once at the beginning of §2 to avoid ambiguity in later thermodynamic expressions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and will make revisions to the manuscript to incorporate explicit verifications where appropriate.

read point-by-point responses

Referee: [§3] §3 (Thermodynamics and entropy derivation): the manuscript states that the first law dM = T dS holds and yields a consistent entropy, yet supplies neither an explicit integration of dM/T for finite SV parameter a nor a Wald-Noether-charge calculation that accounts for the effective stress-energy introduced by the regularization; without this verification the reported phase transitions and merger bounds rest on an unconfirmed identity.

Authors: We thank the referee for this observation. In the manuscript, the entropy was obtained by integrating the first law dS = dM/T, with T computed from the surface gravity of the regularized metric. To make this transparent, we will include the explicit integration in the revised §3, showing the resulting entropy expression for general a. For the Wald-Noether charge method, we agree that it would provide independent confirmation, especially with the effective stress-energy. However, performing a full Wald calculation for this regularized geometry is non-trivial and may require extending the standard formalism. We will add a discussion in the revision explaining the consistency with the first law and note that the entropy matches the expected form. If space permits, we will sketch the Wald approach. revision: partial
Referee: [§4] §4 (Free-energy analysis): the non-trivial phase-transition properties are claimed to depend on the SV parameter, but the absence of an explicitly verified entropy prevents confirmation that the Gibbs free energy G = M − TS is correctly normalized and that the reported swallow-tail behavior is not an artifact of an assumed rather than derived S.

Authors: We agree that the free energy analysis relies on the entropy. With the explicit entropy derivation to be added in §3, the Gibbs free energy G = M - T S will be recomputed and the swallow-tail behavior demonstrated for various a values in the revised §4. This will confirm that the phase transitions are genuine and not artifacts. We will also ensure the normalization is clear by comparing to the Schwarzschild-AdS case. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces the SV-regularization parameter as an external modification to the AdS metric, computes the modified lapse function, derives temperature from surface gravity, and states an entropy formula asserted to satisfy the first law for the regularized geometry. Phase structure follows from standard free-energy analysis in the extended phase space, with explicit comparison to the a=0 limit. No step reduces a claimed prediction or first-principles result to a fitted parameter or self-citation by construction; the central results (non-monotonic bounds on post-merger mass, parameter-dependent phase transitions) are direct consequences of the modified metric functions rather than tautological redefinitions of inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The SV-regularization parameter functions as a free parameter that controls the geometry and all reported thermodynamic and merger results. The validity of the first and second laws for the regularized metric is treated as a domain assumption that is then verified for consistency.

free parameters (1)

SV-regularization parameter
Introduced to remove the central singularity while preserving asymptotic AdS behavior; all phase-transition and merger results depend on its value.

axioms (2)

domain assumption First law of black hole thermodynamics holds for the SV-regularized AdS geometry
Invoked to derive a consistent entropy formula as stated in the abstract.
domain assumption Second law remains valid during equal-mass mergers of SV-regular black holes
Used to constrain post-merger mass as a function of the regularization parameter.

pith-pipeline@v0.9.0 · 5467 in / 1330 out tokens · 45533 ms · 2026-05-17T05:09:03.761507+00:00 · methodology

discussion (0)

Reference graph

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