Localization Instability in the Rotating D-branes

TL;DR

This paper investigates how rotation affects the phase transition between localized and extended black brane solutions in string theory, revealing that angular momentum can induce a localization transition similar to non-rotating cases.

Contribution

It extends the understanding of phase transitions in rotating black branes, showing that angular momentum can trigger localization transitions akin to static cases.

Findings

Localization phase transition occurs at critical angular momentum.

Rotation induces a transition between rotating branes and Kerr black holes.

The topology of the spacetime influences the presence of the phase transition.

Abstract

In the microcanonical ensemble for string theory on $ AdS_m \times 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 $R^2 \times S^{m-2}$. The phase transition will not appear if the $AdS_m$ has the topology $R^2 \times T^{m-2}$, that is, when the $AdS_m\times S^n$ 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.