That has been proven for any non-extremal black hole in d = 4 Einstein gravity coupled to any matter obeying the weak energy condition with hyperbolic equations of motion and asymptotically-flat boundary conditions [161, 163Jump To The Next Citation Point, 254, 86, 143]. The proof has been extended to extremal black holes, to higher dimensions and to anti-de Sitter asymptotics in [171, 170Jump To The Next Citation Point, 85].