Black hole entropy in diffeomorphism-invariant nonminimal gravity decomposes as S_H = S_W + S_1 + ΔS, with the extra terms required for bumblebee and Weyl-vector Gauss-Bonnet solutions but not for regular Kalb-Ramond branches.
Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In extended black hole thermodynamics, the cosmological constant and other couplings are treated as thermodynamic variables, yielding the first law $\tilde{\delta}M = T\tilde{\delta}S+\Omega\tilde{\delta}J +\mathcal{V} \tilde{\delta}P+\cdots$, where $P\equiv -\frac{\Lambda}{8\pi}$. A long-standing conceptual gap in this framework is that, unlike $M$, $T$, $S$, $\Omega$, and $J$, the thermodynamic volume $\mathcal{V} $ lacks a first-principles definition and can only be deduced from other thermodynamic quantities. This deficiency indicates that the underlying origin of $\mathcal{V} $ remains poorly understood. In this paper, we resolve this issue and provide an explicit, covariant formula for $\mathcal{V} $. We demonstrate that $\mathcal{V} $ (and the conjugate quantities of other couplings) universally decomposes into two contributions: one arising from the explicit coupling dependence of the Lagrangian, and the other from the response of the fundamental dynamical fields. This clarifies the physical meaning of the thermodynamic volume and places it on the same footing as other intrinsic thermodynamic quantities.
fields
gr-qc 3years
2026 3representative citing papers
Conserved charges built from a Kerr-Schild background show the first law requires the Killing vector and AdS background to be held fixed, explaining why the rotating-frame energy F fails while E works, and why the geometric volume appears in the β Smarr relation.
An exact dyonic black hole metric is derived in Lorentz-violating gravity with background Kalb-Ramond field and nonminimal EM coupling; geodesics and extended thermodynamics are analyzed showing parameter-dependent shadows and first-order phase transitions.
citing papers explorer
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Black Hole Entropy Beyond the Wald Term in Nonminimally Coupled Gravity: A Covariant Phase Space Decomposition
Black hole entropy in diffeomorphism-invariant nonminimal gravity decomposes as S_H = S_W + S_1 + ΔS, with the extra terms required for bumblebee and Weyl-vector Gauss-Bonnet solutions but not for regular Kalb-Ramond branches.
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The Role of the Volume in Black Hole Thermodynamics
Conserved charges built from a Kerr-Schild background show the first law requires the Killing vector and AdS background to be held fixed, explaining why the rotating-frame energy F fails while E works, and why the geometric volume appears in the β Smarr relation.
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Dyonic Black Holes in Lorentz-Violating Gravity with a Background Kalb--Ramond Field
An exact dyonic black hole metric is derived in Lorentz-violating gravity with background Kalb-Ramond field and nonminimal EM coupling; geodesics and extended thermodynamics are analyzed showing parameter-dependent shadows and first-order phase transitions.