The Gravitational Hamiltonian, Action, Entropy, and Surface Terms

Details The Gravitational Hamiltonian, Action, Entropy, and Surface Terms The Gravitational Hamiltonian, Action, Entropy, and Surface Terms

1995-01-13

arxiv.org/abs/gr-qc/9501014v1

Class.Quant.Grav. 13 (1996) 1487-1498

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, no figures

Scientific paper

10.1088/0264-9381/13/6/017

We give a general derivation of the gravitational hamiltonian starting from the Einstein-Hilbert action, keeping track of all surface terms. The surface term that arises in the hamiltonian can be taken as the definition of the `total energy', even for 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 are horizons of infinite area (e.g. acceleration horizons) as well as the usual finite area black hole horizons. Acceleration horizons seem to be more analogous to extreme than nonextreme black holes, since we find evidence that their horizon area is not related to the total entropy.

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