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arXiv · 2206.08944

An infinity of black holes

Gary T. Horowitz·Diandian Wang·Xiaohua Ye
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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.

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Gary T. Horowitz, Diandian Wang, Xiaohua Ye. 2022-06-17. An infinity of black holes. https://doi.org/10.1088/1361-6382%2Fac994b

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