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

TL;DR

This paper investigates a horizon identity relating Brown-York quasilocal energy and Komar charge in black hole spacetimes, proving its validity for various solutions and conditions in general relativity.

Contribution

It establishes and proves a horizon defining identity involving quasilocal energy and charge for a broad class of black hole solutions, including static, non-static, and non-flat cases.

Findings

The identity holds for spherically symmetric static black holes.

It is valid for asymptotically flat and non-flat solutions.

The identity can be derived from a Gauss-Codacci condition.

Abstract

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.