Black hole mass formula in the membrane paradigm

The membrane paradigm approach adopts a timelike surface, stretched out off the null event horizon, to study several important black hole properties. We use this powerful tool to give a direct derivation of the black hole mass formula in the static and stationary cases without and with electric field. Since here the membrane is a self-gravitating material system, we go beyond the usual applicability on test particles and test fields of the paradigm.