Deforming black holes in AdS

TL;DR

This paper explores how boundary metric deformations influence AdS black hole shapes, revealing that some horizons are insensitive to boundary changes and constructing new solutions to study this response.

Contribution

It analytically links boundary deformations to black hole shape changes and numerically constructs new solutions where horizons respond to boundary geometry variations.

Findings

Deformations of the boundary metric often cause black hole shape changes.

Some black hole horizons are insensitive to large boundary deformations.

Constructed new solutions to analyze horizon response dependence on temperature.

Abstract

We investigate how changes in the boundary metric affect the shape of AdS black holes. Most of our work is analytic and based on the AdS C-metric. Both asymptotically hyperbolic and compact black holes are studied. It has recently been shown that the AdS C-metric contains configurations of highly deformed black holes, and we show that these deformations are usually the result of similar deformations of the boundary metric. However, quite surprisingly, we also find cases where the horizon is insensitive to certain large changes in the boundary geometry. This motivates the search for a new family of black hole solutions with the same boundary geometry in which the horizon does respond to the changes in the boundary. We numerically construct these solutions and we (numerically) explore how the horizon response to boundary deformations depends on temperature.