Rotating Hairy Black Holes in AdS$_5\times$S$^5$

TL;DR

This paper numerically constructs and analyzes rotating, charged hairy black holes in AdS$_5$×S$^5$, revealing their existence near the BPS bound, their phase structure, and implications for dual field theory thermodynamics.

Contribution

It provides the first detailed numerical study of fully non-linear rotating hairy black holes in AdS$_5$×S$^5$, including their phase diagram and supersymmetric limits.

Findings

Hairy black holes exist arbitrarily close to the BPS bound for all charges.

They saturate the BPS bound in the zero and infinite temperature limits.

In the planar limit, a new family of rotating hairy black branes is found.

Abstract

We present a numerical study of fully non-linear, rotating and charged hairy black hole solutions in five-dimensional anti-de Sitter space, which originate from a consistent truncation of $\mathcal{N}=8$ supergravity, and can be consistently embedded in type IIB supergravity with AdS$_5\times$S$^5$ asymptotics. The hairy black holes have one scalar field charged under a $U(1)$ gauge field, and branch from the near-extremal Cveti\v{c}, L\"{u} and Pope solutions. We give numerical evidence that the hairy solutions exist arbitrarily close to the BPS bound for all charges, and saturate it in the $T\rightarrow 0$ and $T\rightarrow\infty$ limits. We give further evidence for the conjecture of Markevi\v{c}i\={u}t\.e and Santos, that on the BPS bound, the rotating hairy black holes form a two-parameter family of solutions with finite entropy, and can be regarded as a one-parameter extension of the supersymmetric Gutowski and Reall black hole. We analyse the approach to the supersymmetric limit and explore the full phase diagram. In the planar horizon limit we find a two parameter family of rotating hairy black brane solutions which cannot be obtained via a Lorentz boost. The field theory dual exhibits a spontaneously generated current. The results of this paper suggest rich and intricate structure of hairy black hole solutions in AdS$_5\times$S$^5$, and highlight their importance in understanding the thermodynamics of $\mathcal{N}=4$ SYM.