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 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.

20 pages, 4 figures, minor typos corrected and references updated in v3

References in corpus (5)

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• Thermodynamic and observational implications of black holes in toroidal geometry
• Probing black hole microstructure with the kinetic turnover of phase transition
• RPST-Inspired Formalism for Black Holes in Flat Spacetime
• Thermodynamics and overcharging problem in the extended phase spaces of charged AdS black holes with cloud of strings and quintessence under charged particle absorption
• P-V criticality of conformal anomaly corrected AdS black holes
• Black-Hole Thermodynamics from Gauge Freedom in Extended Iyer-Wald Formalism
• Surface tension of the horizon
• Complex Plane Phase Diagram and Widom Line for the Born-Infeld Black Holes with Reentrant Phase Transition
• Connections between entropy surface density and microscopic property in black holes
• Thermodynamic Volume Product in Spherically Symmetric and Axisymmetric Spacetime
• Tricritical point and solid/liquid/gas phase transition of higher dimensional AdS black hole in massive gravity
• Extended symmetry of the Maxwell theory with a gauge coupling constant as a conserved charge
• Quantum and higher curvature corrections to the anti-de Sitter black hole
• Angular Momentum-Free of the Entropy Relations for Rotating Kaluza-Klein Black Holes
• On Thermodynamic Stability of Black Holes. Part II: AdS Family of Solutions
• Thermodynamics and orbital structure of anti-de Sitter black holes in Palatini-inspired nonlinear electrodynamics
• Planckian charged black holes and their cosmological ramifications
• Phase transition structure and breaking of universal nature of central charge criticality in a Born-Infeld $AdS$ black hole
• Holographic CFT phase transitions and criticality for charged Gauss-Bonnet AdS black holes in the ensemble at fixed $(C,\mathcal{V},\tilde{Q},\tilde{\mathcal{A}})$
• Modifying horizon thermodynamics by surface tensions
• Hawking atmosphere of anti-de Sitter black holes
• Holographic Extended Thermodynamics of deformed AdS-Schwarzschild black hole