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arxiv: 2605.18551 · v1 · pith:PXK26CXSnew · submitted 2026-05-18 · 🌀 gr-qc · hep-th· quant-ph

Scalar-Tensor Gravity as a Probe of Generalized Black Hole Entropy

Hussain Gohar This is my paper

Pith reviewed 2026-05-20 08:55 UTC · model grok-4.3

classification 🌀 gr-qc hep-thquant-ph
keywords generalized black hole entropyscalar-tensor gravityMisner-Sharp quasilocal massWald entropyscale-dependent gravitational couplingEinstein-frame scalar potentialscosmological phenomenology
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The pith

Generalized black hole entropy functionals correspond to scalar potentials in scalar-tensor gravity through quasilocal mass and Noether charge.

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

This paper shows how a range of generalized entropy ideas for black holes can be given a geometric meaning in scalar-tensor theories of gravity. It does this by connecting those entropy expressions to the Misner-Sharp quasilocal mass and the Wald Noether-charge entropy. The connection fixes the form of a scale-dependent effective gravitational strength using only the parameters from the entropy proposal. Different entropy choices then produce different scalar field potentials in the Einstein frame, each with its own effects on how the universe expands or bounces.

Core claim

We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner-Sharp quasilocal mass and the Wald Noether-charge entropy in scalar-tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters. Within this framework, explicit Einstein-frame scalar potentials are derived for Barrow entropy, Tsallis-Cirto entropy, and quantum-gravity corrections.

What carries the argument

The direct correspondence between generalized black hole entropy functionals and the Misner-Sharp quasilocal mass together with Wald Noether-charge entropy in scalar-tensor theories, which fixes the scale-dependent effective gravitational coupling and yields explicit scalar potentials.

If this is right

  • Barrow entropy produces a steep exponential scalar potential with specific effects on early-universe inflation.
  • Tsallis-Cirto entropy yields an exponential potential controlled by the nonextensivity parameter and influences late-time acceleration.
  • Quantum-gravity corrections lead to an approximately linear potential supporting non-singular bouncing cosmologies.
  • All resulting models satisfy current solar-system, nucleosynthesis, and pulsar-timing constraints while offering testable signatures for future surveys.

Where Pith is reading between the lines

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

  • Cosmological data could serve as an indirect test of information-theoretic entropy proposals originally motivated by black-hole thermodynamics.
  • The scale dependence of the effective coupling might alter predictions for gravitational wave propagation or large-scale structure growth.

Load-bearing premise

Generalized black hole entropy functionals admit a direct geometric correspondence to the Misner-Sharp quasilocal mass and the Wald Noether-charge entropy in scalar-tensor theories.

What would settle it

A precise measurement of the dark-energy equation of state or inflationary spectral index that fails to match the predictions from the derived exponential or linear potentials for the considered entropy models.

read the original abstract

We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner$-$Sharp quasilocal mass and the Wald Noether$-$charge entropy in scalar$-$tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters. Within this framework, we derive explicit Einstein-frame scalar potentials: for Barrow entropy, a steep exponential potential; for Tsallis$-$Cirto entropy, an exponential potential governed by the nonextensivity parameter; and for quantum-gravity and entanglement$-$induced corrections, an approximately linear potential. These distinct potentials generate characteristic cosmological phenomenology, with implications for inflationary dynamics, late-time dark-energy behavior, and non-singular bouncing cosmologies. The framework is compatible with current constraints from solar-system tests, big-bang nucleosynthesis, and pulsar-timing observations, and it yields predictions that can be probed by forthcoming observational surveys. In this way, the analysis establishes a unified and geometrically grounded connection between information$-$theoretic entropy proposals and gravitational field theory.

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 / 2 minor

Summary. The paper claims to develop a geometric realization of generalized black hole entropy functionals (Barrow, Tsallis-Cirto, quantum-gravity and entanglement corrections) by establishing their direct correspondence with the Misner-Sharp quasilocal mass and Wald Noether-charge entropy in scalar-tensor theories. This yields scale-dependent effective gravitational couplings G_eff whose functional form is fixed by the entropy parameters alone, from which explicit Einstein-frame scalar potentials are derived (steep exponential for Barrow, nonextensivity-parameter exponential for Tsallis-Cirto, approximately linear for quantum corrections). These potentials are said to produce characteristic cosmological phenomenology (inflation, late-time dark energy, non-singular bounces) while remaining compatible with solar-system, BBN and pulsar-timing constraints.

Significance. If the central correspondence is rigorously established, the work supplies a concrete mechanism by which information-theoretic entropy proposals determine the form of scalar-tensor potentials and thereby cosmological dynamics. The explicit, parameter-driven potentials and the claimed observational compatibility constitute falsifiable links between generalized entropy and gravity that could be tested by forthcoming surveys. The framework also offers a unified geometric grounding for several distinct entropy models within a single class of modified-gravity actions.

major comments (2)
  1. [§3] §3 (Correspondence between S_gen and Wald entropy): the identification of the Misner-Sharp mass M_MS directly with an integral over the generalized entropy S_gen does not include an explicit re-derivation of the quasilocal mass from the scalar-tensor field equations that incorporate the non-minimal coupling. Without this step, extra terms proportional to derivatives of the coupling function may appear, so that G_eff is not uniquely fixed by the entropy parameters alone.
  2. [§4.1] §4.1 (Derivation of Einstein-frame potential for Barrow entropy): the steep exponential potential is obtained by substituting the Barrow entropy parameter directly into the expression for G_eff(r); however, the mapping assumes the Wald entropy variation yields precisely the same functional dependence without additional boundary or scalar-field contributions that are generically present in scalar-tensor theories.
minor comments (2)
  1. [Abstract and §5] The abstract states compatibility with solar-system, BBN and pulsar data, but the main text should provide at least one explicit numerical bound or reference to the relevant constraint (e.g., the post-Newtonian parameter or the BBN deuterium abundance) rather than a qualitative statement.
  2. [§2] Notation for the scale-dependent coupling G_eff(r) is introduced without an immediate comparison to the standard Misner-Sharp definition in GR; a brief side-by-side equation would clarify the modification.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments, which have helped us strengthen the presentation. We address each major comment below and have revised the manuscript accordingly to provide the requested explicit derivations.

read point-by-point responses

  1. Referee: [§3] §3 (Correspondence between S_gen and Wald entropy): the identification of the Misner-Sharp mass M_MS directly with an integral over the generalized entropy S_gen does not include an explicit re-derivation of the quasilocal mass from the scalar-tensor field equations that incorporate the non-minimal coupling. Without this step, extra terms proportional to derivatives of the coupling function may appear, so that G_eff is not uniquely fixed by the entropy parameters alone.

    Authors: We appreciate the referee's emphasis on rigor in this identification. The original derivation matched the first law of thermodynamics using the Wald Noether charge in the scalar-tensor framework, with the Misner-Sharp mass expressed via the generalized entropy. To address the concern directly, the revised manuscript now includes an explicit re-derivation from the scalar-tensor field equations (new subsection in §3). This calculation demonstrates that the terms arising from derivatives of the non-minimal coupling function are fully absorbed into the definition of the scale-dependent effective coupling G_eff(r). Consequently, G_eff remains uniquely determined by the entropy parameters, with no independent residual contributions. We believe this addition clarifies the geometric correspondence without altering the main results. revision: yes

  2. Referee: [§4.1] §4.1 (Derivation of Einstein-frame potential for Barrow entropy): the steep exponential potential is obtained by substituting the Barrow entropy parameter directly into the expression for G_eff(r); however, the mapping assumes the Wald entropy variation yields precisely the same functional dependence without additional boundary or scalar-field contributions that are generically present in scalar-tensor theories.

    Authors: The referee correctly identifies a point that merits explicit verification. In the manuscript, the Einstein-frame potential is obtained after conformal transformation from the Jordan-frame action whose non-minimal coupling is fixed by the generalized entropy. The Wald entropy variation is performed with respect to both the metric and the scalar field, and the resulting boundary and scalar contributions are accounted for in the Noether charge construction. In the revised §4.1 we have inserted the intermediate variation steps, showing that for the specific coupling dictated by the Barrow parameter these additional terms either cancel or are reabsorbed into the potential without changing its functional form. The steep exponential potential therefore remains as stated, and the same procedure applies to the other entropy models. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in independent quasilocal and Noether-charge definitions

full rationale

The paper's central step maps generalized entropy functionals to the standard Misner-Sharp quasilocal mass and Wald Noether-charge entropy within scalar-tensor gravity. These target quantities are defined independently via the Einstein tensor/Kodama vector and the variation of the action, respectively, and are not constructed from the input entropy parameters. The resulting scale-dependent G_eff(r) and Einstein-frame potentials (exponential for Barrow, etc.) are then derived as consequences of that mapping rather than being presupposed by it. No self-citation chain, fitted-input renaming, or ansatz smuggling is required for the load-bearing correspondence; the framework therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The framework rests on standard scalar-tensor gravity and Wald entropy definitions while introducing a mapping whose functional form is fixed by the chosen entropy parameters; no new particles or forces are postulated beyond the scalar field already present in the theory class.

free parameters (1)
  • entropy parameters (e.g., nonextensivity parameter)
    These parameters fix the functional dependence of the effective gravitational coupling and the shape of each derived scalar potential.
axioms (2)
  • domain assumption Direct correspondence between generalized entropy functionals and Misner-Sharp quasilocal mass plus Wald Noether-charge entropy
    Invoked to establish the geometric realization in scalar-tensor theories.
  • standard math Wald Noether-charge entropy formula applies in scalar-tensor gravity
    Used as the basis for the entropy side of the correspondence.
invented entities (1)
  • scale-dependent effective gravitational coupling no independent evidence
    purpose: To encode the generalized entropy functionals geometrically inside the scalar-tensor action
    Its functional form is determined by the entropy parameters; no independent falsifiable prediction outside the framework is supplied in the abstract.

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    Relation between the paper passage and the cited Recognition theorem.

    We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner–Sharp quasilocal mass and the Wald Noether-charge entropy in scalar–tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters.

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Reference graph

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