Distortion of Schwarzschild-anti-de Sitter black holes to black strings

TL;DR

This paper investigates how Schwarzschild-anti-de Sitter black holes can be distorted into black strings, showing that large distortions are possible without violating thermodynamics or the hoop conjecture, especially in the large mass limit.

Contribution

It demonstrates that large distortions of Schwarzschild-anti-de Sitter black holes can form black strings, extending understanding of black hole topologies in AdS spacetimes.

Findings

Black string solutions emerge as limits of distorted black holes.

Large horizon distortions do not violate thermodynamics.

Prolonged horizon distortions are consistent with the hoop conjecture.

Abstract

Motivated by the existence of black holes with various topologies in four-dimensional spacetimes with a negative cosmological constant, we study axisymmetric static solutions describing any large distortions of Schwarzschild-anti-de Sitter black holes parametrized by the mass $m$. Under the approximation such that $m$ is much larger than the anti-de Sitter radius, it is found that a cylindrically symmetric black string is obtained as a special limit of distorted spherical black holes. Such a prolonged distortion of the event horizon connecting a Schwarzschild-anti-de Sitter black hole to a black string is allowed without violating both the usual black hole thermodynamics and the hoop conjecture for the horizon circumference.