Extended phase space thermodynamics for hairy black holes
Dumitru Astefanesei (Pontificia Universidad Católica de Valparaíso, Instituto de Física, Avenida Brasil 2950, Valparaíso, Chile); Paulina Cabrera (Pontificia Universidad Católica de Valparaíso, Instituto de Física, Avenida Brasil 2950, Valparaíso, Chile); Robert B. Mann (Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada, Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada); Raúl Rojas (Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile)
We expand our earlier results [D. Astefanesei et al., Hairy black hole chemistry, J. High Energy Phys. 11 (2019) 043.] to investigate a general class of exact hairy black hole solutions in Einstein-Maxwell-dilaton gravity. The dilaton is endowed with a potential that originates from an electromagnetic Fayet-Iliopoulos term in extended supergravity in four spacetime dimensions. We present the usual thermodynamics by using the counterterm method supplemented with boundary terms for a scalar field with mixed boundary conditions. We then extend our analysis by considering a dynamical cosmological constant and verify the isoperimetric inequality. We obtain a very rich phase diagram and criticality in both the canonical and grand canonical ensembles. Within string theory, the cosmological constant is related to the radius of the external sphere (of the compactification) and can be interpreted as a modulus. In this context, the existence of a critical value hints to the fact that the thermodynamic properties of black holes in lower dimensions depend on the size of the compactification.