The entropy of a quantum-statistical system which is classically approximated
by a general stationary eternal black hole is studied by means of a
microcanonical functional integral. This approach opens the possibility of
including explicitly the internal degrees of freedom of a physical black hole
in path integral descriptions of its thermodynamical properties. If the
functional integral is interpreted as the density of states of the system, the
corresponding entropy equals calS=AH​/4−AH​/4=0 in the semiclassical
approximation, where AH​ is the area of the black hole horizon. The
functional integral reflects the properties of a pure state.Comment: To appear in the proceedings of the Sixth Canadian Conference on
General Relativiy and Relativistic Astrophysics, 7 pages, Late