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 alpha, the Gauss-Bonnet coupling. For positive alpha and sufficiently large ratio root alpha/L, where L/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 <= beta < 3, where beta = 1 - 8 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 beta = 0.