Non Uniform Black Strings and Critical Dimensions in $AdS_d$

TL;DR

This paper investigates non-uniform black string solutions in anti-de Sitter spacetimes across various dimensions, revealing a critical dimension for phase transitions and unexpected negative tension in certain solutions.

Contribution

It constructs numerical solutions for non-uniform black strings in arbitrary $AdS_d$ and explores their phase structure and properties, including the dependence of critical dimension on horizon size.

Findings

Existence of localized black holes in asymptotically $AdS$ spacetime.

Critical dimension depends on the horizon radius.

Presence of negative tension in small horizon radius solutions.

Abstract

We study the equations of black strings in spacetimes of arbitrary dimensions with a negative cosmological constant and construct numerically non uniform black strings solutions. Our results suggest the existence of a localised black hole in asymptotically locally $AdS$ spacetime. We also present evidences for a dependence of the critical dimension on the horizon radius.The critical dimension represents the dimension where the order of the phase transition between uniform and non uniform black string changes. Finally, we argue that both, the regular asymptotically locally $AdS$ solution and $AdS$ black string solutions with a very small horizon radius, present a negative tension. This turns out to be an unexpected feature of the solutions.