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 T m-2, that is, when the AdS(m) X S-n geometry is regarded as arising from th e near-horizon limit of a black m - 2 brane. In this paper, we argue that w hen the black branes are rotating, the localization phase transition will o ccur between some rotating branes and corresponding Kerr black holes when t he angular momentum reaches its critical value.