The Gravitational Hamiltonian, Action, Entropy, and Surface Terms

Abstract

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.

13 pages, no figures

References in corpus (9)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Entropy, Area, and Black Hole Pairs
• A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
• Temperature, Energy, and Heat Capacity of Asymptotically Anti-De Sitter Black Holes
• Duality between Electric and Magnetic Black Holes
• Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
• On Pair Creation of Extremal Black Holes and Kaluza-Klein Monopoles
• Action and Entropy of Extreme and Non-Extreme Black Holes
• Topology, Entropy and Witten Index of Dilaton Black Holes

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