Speaker
Description
Thermodynamic volume and extensivity in black hole thermodynamics
Black holes lack a coordinate-independent notion of volume, so their thermodynamics is non-extensive. In extended AdS thermodynamics, the mass is treated as enthalpy and the cosmological constant as pressure, but for Schwarzschild-AdS black holes, the resulting volume is fixed by the entropy, leaving the state space degenerate. This degeneracy can be resolved by assuming Euler homogeneity of the entropy through a scaling relation between horizon radius, energy and volume. A generalized pressure then selects a volume consistent with the Christodoulou–Rovelli concept. Within this framework, thermodynamic stability is restored, the concavity of the entropy is recovered, and the stability and evaporation boundaries, including the Hawking–Page temperature, shift relative to the standard treatment. Our results complement the quasi-local, holographic definition of black hole volume recently proposed, where boundary area plays the role of volume and extensivity emerges in a large-system limit. Both approaches resolve the state-space degeneracy, but differ on whether volume is an interior or a boundary property.