The First Law of Black Hole Mechanics

Details The First Law of Black Hole Mechanics The First Law of Black Hole Mechanics

1993-05-25

arxiv.org/abs/gr-qc/9305022v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, to appear in Misner Festschrift

Scientific paper

A simple proof of a strengthened form of the first law of black hole mechanics is presented. The proof is based directly upon the Hamiltonian formulation of general relativity, and it shows that the the first law variational formula holds for arbitrary nonsingular, asymptotically flat perturbations of a stationary, axisymmetric black hole, not merely for perturbations to other stationary, axisymmetric black holes. As an application of this strengthened form of the first law, we prove that there cannot exist Einstein-Maxwell black holes whose ergoregion is disjoint from the horizon. This closes a gap in the black hole uniqueness theorems.

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