Optimal Choices of Reference for Quasi-local Energy

TL;DR

This paper proposes a method to determine the reference point for quasi-local energy in covariant Hamiltonian formalism and tests it on spherically symmetric spacetimes, revealing observer-dependent energy values including positive, zero, or negative.

Contribution

It introduces a new program for selecting the reference in quasi-local energy calculations and demonstrates its application to spherically symmetric spacetimes.

Findings

Quasi-local energy varies with observer, being positive, zero, or negative.

The observer measuring maximum energy was identified.

Maximum energy observer's measurements are positive in key spacetimes.

Abstract

We have proposed a program for determining the reference for the quasi-local energy defined in the covariant Hamiltonian formalism. Our program has been tested by applying it to the spherically symmetric spacetimes. With respect to different observers we found that the quasi-local energy can be positive, zero, or even negative. The observer measuring the maximum energy was identified; the associated energy is positive for both the Schwarzschild and the Friedmann-Lema\^{i}tre-Robertson-Walker spacetimes.