BLACK-HOLE ENTROPY AND THE HAMILTONIAN-FORMULATION OF DIFFEOMORPHISM INVARIANT THEORIES

Path integral methods are used to derive a general expression for the entropy of a black hole in a diffeomorphism invariant theory. The resu lt, which depends on the variational derivative of the Lagrangian with respect to the Riemann tensor, agrees with the result obtained from N oether charge methods by Iyer and Wald. The method used here is based on the direct expression of the density of states as a path integral ( the microcanonical functional integral). The analysis makes crucial us e of the Hamiltonian form of the action. An algorithm for placing the action of a diffeomorphism invariant theory in Hamiltonian form is pre sented. Other path integral approaches to the derivation of black hole entropy include the Hilbert action surface term method and the conica l deficit angle method. The relationships between these path integral methods are presented.