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

Sukanta Bose, Naresh Dadhich
1999 Physical Review D, Particles and fields  
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
more » ... ty. 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.
doi:10.1103/physrevd.60.064010 fatcat:y7rezgxamvehnmmrh5e65i6cfm