Penrose inequalities and the stability of non-uniform black strings

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In this talk I will first review static black holes in
Kaluza-Klein theory. It is well-known that within this theory there exist black
strings which are non-uniform along the Kaluza-Klein circle. Using numerical
methods, I will explain how to construct (for the first time) non-uniform black
strings in D>10, where D is the total number of spacetime dimensions. The
stability of such black objects has not been discussed before, and in the last
part of the talk I will explain how one can study the stability of non-uniform
black strings using Penrose inequalities. This will lead to a new conjecture
for the phase diagram of static Kaluza-Klein black holes.