Localization instability in the rotating D-branes

In the microcanonical ensemble for string theory on AdS(m) X S-n, there is a phase transition between a black hole solution extended over the S-n and a solution localized on the S-n if the AdS(m) has the topology R-2 X Sm-2. The phase transition will not appear if the AdS(m) has the topology R-2 X Tm-2, that is, when the AdS(m) X S-n geometry is regarded as arising from the near-horizon limit of a black m - 2 brane. In this paper, we argue that when the black branes are rotating, the localization phase transition will occur between some rotating branes and corresponding Kerr black holes when the angular momentum reaches its critical value.