AdS Dyonic Black Hole and its Thermodynamics

Abstract

We obtain spherically-symmetric and $\R^2$-symmetric dyonic black holes that are asymptotic to anti-de Sitter space-time (AdS), which are solutions in maximal gauged four-dimensional supergravity, with just one of the U(1) fields carrying both the electric and magnetic charges $(Q,P)$. We study the thermodynamics, and find that the usually-expected first law does not hold unless P=0, Q=0 or P=Q. For general values of the charges, we find that the first law requires a modification with a new pair of thermodynamic conjugate variables. We show that they describe the scalar hair that breaks some of the asymptotic AdS symmetries.

21 pages, typos corrected, discussion of Euclidean action added