Abstract
The generalized second law of black-hole thermodynamics was proved by Frolov and Page [Phys. Rev. Lett. 71, 3902 (1993)] for a quasistationary eternal black hole. However, realistic black holes arise from gravitational collapse, and in this case their proof does not hold. In this paper we prove the generalized second law for a quasistationary black hole that arises from gravitational collapse.