Horizon energy and angular momentum from a Hamiltonian perspective

TL;DR

This paper develops a Hamiltonian framework for defining quasilocal energy and angular momentum on horizons in general relativity, aligning with existing horizon formalisms and providing a local perspective.

Contribution

It introduces a Hamiltonian approach to horizon energy and angular momentum using three-surfaces foliated by two-surfaces of zero outward null expansion.

Findings

Provides expressions for quasilocal energy and angular momentum.

Aligns with isolated and dynamical horizon frameworks.

Offers a local boundary formulation in general relativity.

Abstract

Classical black holes and event horizons are highly non-local objects, defined in terms of the causal past of future null infinity. Alternative, (quasi)local definitions are often used in mathematical, quantum, and numerical relativity. These include apparent, trapping, isolated, and dynamical horizons, all of which are closely associated to two-surfaces of zero outward null expansion. In this paper we show that three-surfaces which can be foliated with such two-surfaces are suitable boundaries in both a quasilocal action and a phase space formulation of general relativity. The resulting formalism provides expressions for the quasilocal energy and angular momentum associated with the horizon. The values of the energy and angular momentum are in agreement with those derived from the isolated and dynamical horizon frameworks.