Canonical variables and quasilocal energy in general relativity

TL;DR

This paper introduces Ashtekar-type variables for the two-boundary in general relativity, providing elegant alternative expressions for quasilocal energy and momentum, and unifies different boundary variable frameworks using Sparling forms.

Contribution

It presents Ashtekar-type variables on the two-boundary, offering new expressions for quasilocal surface densities and unifying boundary variable formalisms in general relativity.

Findings

Ashtekar-type variables yield elegant expressions for quasilocal energy and momentum.

Boundary variables can be incorporated into a unified framework using Sparling forms.

The approach simplifies the analysis of boundary contributions in general relativity.

Abstract

Recently Brown and York have devised a new method for defining quasilocal energy in general relativity. Their method yields expressions for the quasilocal energy and momentum surface densities associated with the two-boundary of a spacelike slice of a spatially bounded spacetime. These expressions are essentially Arnowitt-Deser-Misner variables, but with canonical conjugacy defined with respect to the time history of the two-boundary. This paper introduces Ashtekar-type variables on the time history of the two-boundary and shows that these variables lead to elegant alternative expressions for the quasilocal surface densities. In addition, it is demonstrated here that both the boundary ADM variables and the boundary Ashtekar-type variables can be incorporated into a larger framework by appealing to the tetrad-dependent Sparling differential forms.