THE GRAVITATIONAL HAMILTONIAN, ACTION, ENTROPY AND SURFACE TERMS

We give a derivation of the gravitational Hamiltonian starting from th e Einstein-Hilbert action, keeping track of all surface terms. This de rivation can be applied to any spacetime that asymptotically approache s a static background solution. The surface term that arises in the Ha miltonian can be taken as the definition of the 'total energy', even f or spacetimes that are not asymptotically flat. (In the asymptotically flat case, it agrees with the usual ADM energy.) We also discuss the relation between the Euclidean action and the Hamiltonian when there a re horizons of infinite area (e.g. acceleration horizons) as well as t he usual finite area black hole horizons. Acceleration horizons seem t o be more analogous to extreme than nonextreme black holes, since we f ind evidence that their horizon area is not related to the total entro py.