An infinity of black holes

TL;DR

This paper explores the existence of infinitely many static black hole solutions in higher-dimensional anti-de Sitter spaces, revealing complex phase structures and implications for dual field theories.

Contribution

It demonstrates that the number of black hole solutions in certain higher-dimensional AdS spaces can become infinite depending on boundary geometry parameters.

Findings

Number of black hole families depends on boundary sphere ratio

Infinite solutions emerge as ratio approaches a critical value

Implications for phase transitions and dual field theories

Abstract

In general relativity (without matter), there is typically a one parameter family of static, maximally symmetric black hole solutions labelled by their mass. We show that there are situations with many more black holes. We study asymptotically anti-de Sitter solutions in six and seven dimensions having a conformal boundary which is a product of spheres cross time. We show that the number of families of static, maximally symmetric black holes depends on the ratio, $\lambda$, of the radii of the boundary spheres. As $\lambda$ approaches a critical value, $\lambda_{c}$, the number of such families becomes infinite. In each family, we can take the size of the black hole to zero, obtaining an infinite number of static, maximally symmetric non-black hole solutions. We discuss several applications of these results, including Hawking-Page phase transitions and the phase diagram of dual field theories on a product of spheres, new positive energy conjectures, and more.