  The microcanonical functional integral for an eternal black hole system is
considered. This requires computing the microcanonical action for a spatially
bounded spacetime region when its two disconnected timelike boundary surfaces
are located in different wedges of the Kruskal diagram. The path integral is a
sum over Lorentzian geometries and is evaluated semiclassically when its
boundary data are chosen such that the system is approximated by any
Lorentzian, stationary eternal black hole. 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 ${\cal S} = A_H/4 - A_H/4 = 0$ in the
semiclassical approximation, where $A_H$ is the area of the black hole horizon.
The functional integral reflects the properties of a pure state. The
description of the black hole density of states in terms of the eternal black
hole functional integral is also discussed.
