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Where is the PdV term in the first law of black hole thermodynamics?

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arxiv 1209.1272 v3 pith:XNXKDPJK submitted 2012-09-06 gr-qc hep-th

Brian P. Dolan This is my paper
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keywords firstblackblack-holeholeincludephaseresultsthermodynamics
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Traditional treatments of the first law of black hole thermodynamics do not include a discussion of pressure and volume. We give an overview of recent developments proposing a definition of volume that can be used to extend the first law to include these appropriately. New results are also presenting relating to the critical point and the associated second order phase transition for a rotating black-hole in four-dimensional space-time which is asymptotically anti-de Sitter. In line with known results for a non-rotating charged black-hole, this phase transition is shown to be of Van der Waals type with mean field exponents.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Penrose-Rindler equation and horizon thermodynamics of stationary black holes

    gr-qc 2026-02 conditional novelty 6.0 of 10

    For static and Kerr-like rotating black holes the horizon condition is equivalent to the Penrose–Rindler equation, which, read as a pressure equilibrium, yields a quasi-local Smarr formula with a newly defined 'Smarr volume.'

  2. Black-Hole Thermodynamics from Gauge Freedom in Extended Iyer-Wald Formalism

    gr-qc 2025-07 conditional novelty 6.0 of 10

    Exact isohomogeneous transformations, realized by Killing-vector and gauge choices in an extended Iyer-Wald formalism, produce integrable first laws and recover standard Kerr-AdS thermodynamics.

  3. The Role of the Volume in Black Hole Thermodynamics

    gr-qc 2026-06 unverdicted novelty 5.0 of 10

    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 geo...

  4. Joule-Thomson Effect and Geodesic Structure of Charged AdS Black Holes in f(R,T) Coupled with Nonlinear Electrodynamics

    gr-qc 2026-07 conditional novelty 4.0 of 10

    Charge most strongly controls JT inversion and cooling domains of the f(R,T)-NLED AdS black hole; NLED and modified-gravity parameters supply only sub-leading corrections that leave exterior geodesics close to RN-AdS.

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