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

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.