  In gravitational thermodynamics, the entropy of a black hole with distinct
surface gravities can be evaluated in a microcanonical ensemble. At the $WKB$
level, the entropy becomes the negative of the Euclidean action of the
constrained instanton, which is the seed for the black hole creation in the
no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite
universal formula in Euclidean quantum gravity that the entropy of a
nonrotating black hole is one quarter the sum of the products of the Euler
characteristics and the areas of the horizons. For Lovelock gravity, the
entropy and quantum creation of a black hole are also studied.
