Stability of Ads Black Strings

This decade has witnessed a growing interest for solutions of general relativity in AdS spaces. This is due to the celebrated AdS/CFT correspondance conjecture1, relating solutions of general relativity in asymptotically AdS spaces to conformal field theories defined on the conformal boundary of the AdS space. In this context, black hole solutions play an important role2. In more than four dimensional spacetime, the uniqueness theorem on black holes, garantying that the horizon topology of a black object is always S is no longer true. Various black objects have been constructed in higher dimensions, such as black strings with horizon topology S × S in contrast with black holes with horizon topology S. On the other hand, in 1993, R. Gregory and R. Laflamme have shown that black strings and branes are unstable towards long wavelength perturbations3. The Gregory-Laflamme instability was originally discovered in the framework of asymptotically locally flat spacetimes but it is believed to be a generic feature of black extended objects. In particular, it will be argued that this instability persists in asymptotically locally AdS spacetimes, where a black string solution has been found recently by R. Mann, E. Radu and C. Stelea4. This proceeding is organised as follows: we review the black string instability and phase diagram in asymptotically locally flat spacetimes in section 2 before turning to asumptotically locally AdS spacetimes in section 3.