  The authors have recently proposed a ``microcanonical functional integral"
representation of the density of quantum states of the gravitational field. The
phase of this real--time functional integral is determined by a
``microcanonical" or Jacobi action, the extrema of which are classical
solutions at fixed total energy, not at fixed total time interval as in
Hamilton's action. This approach is fully general but is especially well suited
to gravitating systems because for them the total energy can be fixed simply as
a boundary condition on the gravitational field. In this paper we describe how
to obtain Jacobi's action for general relativity. We evaluate it for a certain
complex metric associated with a rotating black hole and discuss the relation
of the result to the density of states and to the entropy of the black hole.
(Dedicated to Yvonne Choquet-Bruhat in honor of her retirement.)
