Perturbative non uniform black strings in ${AdS}_6$

TL;DR

This paper constructs non-uniform AdS black string solutions in six dimensions using perturbation theory, revealing how their thermodynamics are influenced by the AdS curvature, especially for different horizon sizes.

Contribution

It introduces a second-order perturbative approach to analyze non-uniform black strings in AdS_6, providing the first relevant thermodynamic corrections in this context.

Findings

Second-order backreaction corrections to thermodynamics.

Similar properties to flat case for small horizon and length.

AdS curvature impacts thermodynamics for large length configurations.

Abstract

We construct the non uniform AdS black string solution with a perturbation theory in six dimensions, focusing on the backreacting second order correction. The backreactions at second order give the first relevant corrections to the thermodynamical quantities. Our results show that for configurations with horizon radius and length in the extradimension small compared to the AdS radius, the properties of the non uniform black string are similar to the locally asymptotically flat case. For black strings with small horizon radial coordinate but large length in the extradimension, the thermodynamical properties of the solutions are affected by the AdS curvature.