The fate of black branes in Einstein-Gauss-Bonnet gravity

Black branes are studied in Einstein-Gauss-Bonnet (EGB) gravity. Evaporation drives black branes towards one of two singularities depending on the sign of $\alpha$, the Gauss-Bonnet coupling. For positive $\alpha$ and sufficiently large ratio $\sqrt{\alpha }\mathrm{/}L$, where $L\mathrm{/}2\pi$ 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 $\alpha$ all black branes encounter the GL instability. No black branes may exist outside of the interval of the critical values, $0\le \beta <3$, where $\beta =1-8\alpha \mathrm{/}{r}_h^2$ 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 $\beta =0$.