A Hamiltonian Approach to the Mass of Isolated Black Holes

TL;DR

This paper introduces a Hamiltonian-based, quasi-local definition of black hole mass that applies to isolated horizons in Einstein-Maxwell theory, aligning with known solutions and Bondi energy under specific conditions.

Contribution

It proposes a novel Hamiltonian approach to defining the mass of isolated black hole horizons without relying on asymptotic infinity, connecting it to Bondi energy.

Findings

Mass matches Reissner-Nordstrom solution values

Mass equals future limit of Bondi energy under assumptions

Provides a local, Hamiltonian-based mass definition

Abstract

Boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon. Inspired by Hamiltonian mechanics, a (quasi-)local definition of isolated horizon mass is formulated. Although its definition does not refer to infinity, this mass takes the standard value in a Reissner-Nordstrom solution. Furthermore, under certain technical assumptions, the mass of an isolated horizon is shown to equal the future limit of the Bondi energy.