On the Brown-York quasilocal energy, gravitational charge, and black hole horizons

Details On the Brown-York quasilocal energy, gravitational charge, and black hole horizons On the Brown-York quasilocal energy, gravitational charge, and black hole horizons

1999-06-16

arxiv.org/abs/gr-qc/9906063v1

Phys.Rev. D60 (1999) 064010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, RevTex. To appear in Physical Review D

Scientific paper

10.1103/PhysRevD.60.064010

We study a recently proposed horizon defining identity for certain black hole spacetimes. It relates the difference of the Brown-York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime. The Brown-York quasilocal energy is evaluated for some specific choices of spacetime foliations. With a certain condition imposed on the matter distribution, we prove this identity for spherically symmetric static black hole solutions of general relativity. For these cases, we show that the identity can be derived from a Gauss-Codacci condition that any three-dimensional timelike boundary embedded around the hole must obey. We also demonstrate the validity of the identity in other cases by explicitly applying it to several static, non-static, asymptotically flat, and asymptotically non-flat black hole solutions. These include the asymptotically FRW solutions and the case of a black hole with a global monopole charge.

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