  In gravitational thermodynamics, the origin of a black hole's entropy is the
topology of its instanton or constrained instanton. We prove that the entropy
of an arbitrary nonrotating black hole is one quarter the sum of the products
of the Euler characteristics of its horizons with their respective areas. The
Gauss-Bonnet-like form of the action is not only crucial for the evaluation,
but also for the existence of the entropy. This result covers all previous
results on the entropy of a nonrotating black hole with a regular instanton.
The argument can be readily extended into the lower or higher dimensional
model. The problem of quantum creation of such a black hole is completely
resolved.
