Pressure and volume in the first law of black hole thermodynamics
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 fourdimensional 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2011
 DOI:
 10.1088/02649381/28/23/235017
 arXiv:
 arXiv:1106.6260
 Bibcode:
 2011CQGra..28w5017D
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 20 pages, 4 figures, minor typos corrected and references updated in v3