Abstract

We expand our earlier results [D. Astefanesei, Hairy black hole chemistry, J. High Energy Phys. 11 (2019) 043.JHEPFG1029-847910.1007/JHEP11(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 N=2 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. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.