Non Uniform Black Strings and Critical Dimensions in AdS(d)

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.