Fate of black branes in Einstein-Gauss-Bonnet gravity

Black branes are studied in Einstein-Gauss-Bonnet gravity. Evaporation drives black branes toward one of two singularities depending on the sign of α, the Gauss-Bonnet coupling. For positive α and sufficiently large ratio √α/L, where L/2π 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 α all black branes encounter the GL instability. No black branes may exist outside of the interval of the critical values 0≤β<3, where β=1-8α/rₕ² and rₕ 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 β=0.