Quasilocal energy conditions

TL;DR

This paper introduces a quasilocal dominant energy condition derived from the local dominant energy condition, which has implications for the positivity and physical interpretation of quasilocal energy in gravitational systems.

Contribution

It formulates a new quasilocal dominant energy condition based on the local dominant energy condition, extending the understanding of energy positivity in gravitational theories.

Findings

Derives a quasilocal dominant energy condition from the local dominant energy condition.

Shows that the quasilocal energy is not necessarily positive definite.

Establishes a quasilocal weak energy condition as a consequence.

Abstract

The classical value of the Hamiltonian for a system with timelike boundary has been interpreted as a quasilocal energy. This quasilocal energy is not positive definite. However, we derive a `quasilocal dominant energy condition' which is the natural consequence of the local dominant energy condition. We discuss some implications of this quasilocal energy condition. In particular, we find that it implies a `quasilocal weak energy condition'.