Critical bubbles and implications for critical black strings
  We demonstrate the existence of gravitational critical phenomena in higher dimensional electrovac bubble spacetimes. To this end, we study linear fluctuations about families of static, homogeneous spherically symmetric bubble spacetimes in Kaluza-Klein theories coupled to a Maxwell field. We prove that these solutions are linearly unstable and posses a unique unstable mode with a growth rate that is universal in the sense that it is independent of the family considered. Furthermore, by a double analytical continuation this mode can be seen to correspond to marginally stable stationary modes of perturbed black strings whose periods are integer multiples of the Gregory-Laflamme critical length. This allow us to rederive recent results about the behavior of the critical mass for large dimensions and to generalize them to the charged black string case. 
Olivier Sarbach and Luis Lehner