AdS Dyonic Black Hole and its Thermodynamics

TL;DR

This paper constructs and analyzes dyonic black hole solutions in AdS space within supergravity, revealing that their thermodynamics require modifications to the first law due to scalar hair effects.

Contribution

It introduces new dyonic black hole solutions in AdS supergravity and identifies necessary modifications to their thermodynamic first law for general charges.

Findings

Standard first law fails unless P=0, Q=0, or P=Q.

A modified first law includes new conjugate variables.

Scalar hair breaks some asymptotic AdS symmetries.

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.