Pressure and volume in the first law of black hole thermodynamics

By Brian P. Dolan. 2011

726 citations recorded by the source corpus.

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 spacetime 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 black hole this figure is reduced to 52%, compared to the corresponding values of 50% and 29% respectively when the cosmological constant is zero.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e8c5ab5f280a9cf58825bec49c4301adef8df9d0

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Citations in the corpus

Holographic heat engines (2014, neutral): “[5–13], including the reviews in refs.”
Multiple reentrant phase transitions and triple points in Lovelock thermodynamics (2014, background): “Finally, comparing the physics of black holes with real world thermodynamic systems becomes a much more reasonable possibility [37], insofar as tricriticality, reentrant phase transitions, and Van der Waals behaviour all have counterparts in laboratory physics [4, 5, 6, 7, 13, 20, 21]; an extensive ”
Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization (2012, neutral): “3) The thermodynamics of charged rotating black holes treating the cosmological constant as independent variable was performed in [7, 9, 15].”
Extended phase space thermodynamics for third-order Lovelock black holes in diverse dimensions (2014, background): “Recently, the idea of including the cosmological constant in the first law of black hole has become popular [5–8].”
Black hole chemistry: thermodynamics with Lambda (2016, background): “22 more complete since it allows proper identification between intensive and extensive variables [72, 73].”
Holographic entanglement entropy and the extended phase structure of STU black holes (2015, background): “In a recent series of papers, the analogy with the Van der Waals gas has been made more precise in the framework of extended black hole thermodynamics [8–25].”
Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume (2014, background): “This has led to a number of investigations of black hole thermodynamics in this extended phase space [5–39].”
Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes (2013, background): “[5] B.”