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Pressure and volume in the first law of black hole thermodynamics

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30 Pith papers citing it
570 external citations · Pith
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abstract

The mass of a black hole is interpreted, in terms of thermodynamic potentials, as being the enthalpy, with the pressure given by the cosmological constant. The volume is then defined as being the Legendre transform of the pressure and the resulting relation between volume and pressure is explored in the case of positive pressure. A virial expansion is developed and a van der Waals like critical point determined. The first law of black hole thermodynamics includes a PdV term which modifies the maximal efficiency of a Penrose process. It is shown that, in four dimensional space-time with a negative cosmological constant an extremal charged rotating black hole can have an efficiency of up to 75%, while for an electrically neutral rotating back hole this figure is reduced to 52%, compared to the corresponding values of 50% and 29% respectively when the cosmological constant is zero.

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representative citing papers

Black hole equations of state and response functions

hep-th · 2026-06-15 · unverdicted · novelty 6.0

Applies a thermodynamic representation framework to quasi-local Schwarzschild black holes, deriving representation-dependent stability, negative thermal expansion, and cooling under isenthalpic expansion.

Gravitational constant as a conserved charge in black hole thermodynamics

hep-th · 2025-09-10 · conditional · novelty 6.0

Using two scalar-gauge pairs and the off-shell ADT formalism in a modified Einstein-Hilbert theory, the authors derive conserved charges for mass, cosmological constant, and G that yield a consistent extended thermodynamic first law and Smarr formula.

Rotating End of the World

hep-th · 2026-04-26 · unverdicted · novelty 6.0

Dynamical EoW branes in rotating BTZ black holes are mapped to JT gravity, yielding BCFT thermodynamics and indicating possible interior transitions between single and double-joint configurations.

Holographic Stirling engines and the route to Carnot efficiency

hep-th · 2026-04-17 · unverdicted · novelty 6.0

Stirling efficiency reaches Carnot when fixed-volume heat capacity is volume-independent, true for classical gases but not quantum or CFTs; holographic CFTs approach Carnot at large potentials with faster convergence under regeneration.

The Role of the Volume in Black Hole Thermodynamics

gr-qc · 2026-06-29 · conditional · novelty 5.0

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.

Holographic pressure and volume for black holes

hep-th · 2026-02-04 · unverdicted · novelty 5.0

Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.

Hawking atmosphere of anti-de Sitter black holes

gr-qc · 2026-05-22 · unverdicted · novelty 4.0

Applies Parikh-Wilczek tunneling with backreaction to evaporating AdS black holes, finding luminosity deviates from blackbody scaling for small masses due to rapid mass loss, and computes renormalized energy-momentum tensor in Vaidya-AdS.

Quantum-statistical constraints on Kerr-anti-de Sitter thermodynamics

gr-qc · 2026-05-15 · unverdicted · novelty 4.0

Quantum-statistical constraints restrict the infinite family of KadS thermodynamic descriptions to a subclass that reduces to Schwarzschild-AdS and Kerr cases in appropriate limits, with uniqueness for co-rotating and volume-coincident descriptions.

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