Covariant Hamiltonian boundary term: Reference and quasi-local quantities

TL;DR

This paper develops a covariant Hamiltonian boundary term framework in general relativity to define quasi-local physical quantities, using isometric matching and energy extremization to specify reference states.

Contribution

It introduces a new method for determining reference values in Hamiltonian boundary terms via 4D isometric matching and energy extremization in Einstein's GR.

Findings

Proposes a covariant boundary term for Einstein's GR.

Uses isometric matching to fix reference metrics.

Extremizes energy to determine optimal reference values.

Abstract

The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the quasi-local quantities: energy-momentum, angular-momentum and center-of-mass. The boundary term depends not only on the dynamical variables but also on their reference values; the latter determine the ground state (having vanishing quasi-local quantities). For our preferred boundary term for Einstein's GR we propose 4D isometric matching and extremizing the energy to determine the reference metric and connection values.