The entropy increase during the black hole formation

The entropy increases enormously when a star collapses into a black hole. For the radiation dominated star, the temperature has decreased from the almost gravitational equilibrium one to the so-called black hole temperature. If we interpret this temperature decrease as the volume increase of the black hole, the entropy increase could be understood as the free expansion of radiation throughthe increased volume. The expected volume size is tentatively estimated. Under this interpretation, it is derived that the entropy is proportional to the horizon surface area and the microscopic states of the black hole entropy could be understood as the statistical states of the enlarged phase space.