Back Reaction of the Hawking Radiation

Three fundamental papers by G.A. Vilkovisky: ``Kinematics of evaporating black holes,'' ``Radiation equations for black holes,'' and ``Backreaction of the Hawking radiation'' (respectively available from arXiv:hep-th/0511182/3/4) present the calculation of the evolution of black holes driven by the Hawking radiation. The solution of the backreaction problem is a generalization of the Schwarzschild metric. Bryce DeWitt had been hoping that the solution of the backreaction problem would be obtained in time for him to include it in his book ``The Global Approach to Quantum Field Theory'' The Hawking radiation and its backreaction are semiclassical effects. According to Vilkovisky, blackloles create a ``vacuum matter charge'' to protect themselves from the quantum evaporation. A spherically symmetric black hole having initially no ``matter charges'' radiates away about 10{\%} of the initial mass and comes to a state in which the vacuum-induced charge equals the remaining mass. The metric in the semiclassical region of the collapse spacetime is obtained and studied. I shall present and discuss Vilkovisky's work.