Fate of black branes in Einstein-Gauss-Bonnet gravity

Abstract

Black branes are studied in Einstein-Gauss-Bonnet gravity. Evaporation drives black branes toward one of two singularities depending on the sign of $\ensuremath{\alpha}$, the Gauss-Bonnet coupling. For positive $\ensuremath{\alpha}$ and sufficiently large ratio $\sqrt{\ensuremath{\alpha}}/L$, where $L/2\ensuremath{\pi}$ is the radius of compactification, black branes avoid the Gregory-Laflamme (GL) instability before reaching a critical state. No black branes with the radius of horizon smaller than the critical value can exist. Approaching the critical state branes have a nonzero Hawking temperature. For negative $\ensuremath{\alpha}$ all black branes encounter the GL instability. No black branes may exist outside of the interval of the critical values $0\ensuremath{\le}\ensuremath{\beta}<3$, where $\ensuremath{\beta}=1\ensuremath{-}8\ensuremath{\alpha}/{r}_{h}^{2}$ and ${r}_{h}$ is the radius of horizon of the black brane. The first order phase transition line of GL transitions ends in a second order phase transition point at $\ensuremath{\beta}=0$.