BOUNDARY STATES AND BLACK-HOLE ENTROPY

A formal derivation of black hole entropy is given as a sum over bound ary states. The boundary states are labeled by energy and momentum sur face densities, and parametrized by the boundary metric. The sum over state labels is expressed as a functional integral with measure determ ined by the density of states. The sum over metrics is expressed as a functional integral with measure determined by the universal expressio n for the inverse temperature gradient at the horizon. The analysis ap plies to any stationary, nonextreme black hole in any theory of gravit ational and matter fields. [S0556-2821(98)04704-3].