The cosmological constant and the black hole equation of state

Understand

The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state.

• The black hole mass is then identified with the enthalpy, rather than the internal energy, and heat capacities are calculated at constant pressure not at constant volume.
• The Euclidean action is associated with a bridge equation for the Gibbs free energy and not the Helmholtz free energy.
• Quantum corrections to the enthalpy and the equation of state of the BTZ black hole are studied.