New stable phase of non uniform black strings in ${AdS}_d$

TL;DR

This paper investigates the phase structure of non-uniform AdS black strings using perturbative and preliminary non-perturbative methods, revealing a potential new stable phase characterized by long non-uniform strings.

Contribution

It introduces a perturbative analysis of non-uniform AdS black strings up to second order and provides initial insights into the non-perturbative phase diagram, suggesting a new stable phase.

Findings

Identification of a new stable long non-uniform black string phase

Perturbative corrections significantly affect thermodynamical properties

Initial phase diagram mapping of non-uniform versus uniform black strings

Abstract

We consider the non uniform $AdS$ black string equations in arbitrary number of dimension in a perturbative approach up to order 2 and in a non perturbative. We restrict the study in the perturbative approach to the backreacting modes, since they provide the first relevant corrections on the thermodynamical quantities of the solutions. We also present some preliminary results in the construction of non-perturbative solutions, in particular, we present a first part of the non uniform - uniform black string phase diagram. Our results suggests the existence of a new stable phase for $AdS$ non uniform black strings, namely long non uniform black string, with the extra direction length of the order of the $AdS$ curvature.