AN OPERATIONAL APPROACH TO BLACK-HOLE ENTROPY

In this paper we calculate the entropy of a thin spherical shell that contracts reversibly from infinity down to its event horizon. We find that, for a broad class of equations of state, the entropy of a non-ex tremal shell is one-quarter of its area in the black hole limit. The c onsiderations in this paper suggest the following operational definiti on for the entropy of a black hole: S-BH is the equilibrium thermodyna mic entropy that would be stored in the material which gathers to form the black hole, if all of this material were compressed into a thin l ayer near its gravitational radius. Since the entropy for a given mass and area is maximized for thermal equilibrium we expect that this is the maximum entropy that could be stored in the material before it cro sses the horizon. In the case of an extremal black hole the shell mode l does not assign an unambiguous value to the entropy.