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

Understand

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.