Pseudotensors and quasilocal energy-momentum

TL;DR

This paper explores the relationship between pseudotensors and quasilocal energy-momentum in gravitating systems, demonstrating that pseudotensors can be viewed as specific Hamiltonian boundary terms, thus establishing their quasilocal nature.

Contribution

It shows that pseudotensors are equivalent to Hamiltonian boundary terms, providing a quasilocal interpretation and clarifying boundary conditions for well-known pseudotensors.

Findings

Pseudotensors correspond to Hamiltonian boundary terms.

Pseudotensors are quasilocal energy-momentum densities.

Boundary conditions are identified for known pseudotensors.

Abstract

Early energy-momentum investigations for gravitating systems gave reference frame dependent pseudotensors; later the quasilocal idea was developed. Quasilocal energy-momentum can be determined by the Hamiltonian boundary term, which also identifies the variables to be held fixed on the boundary. We show that a pseudotensor corresponds to a Hamiltonian boundary term. Hence they are quasilocal and acceptable; each is the energy-momentum density for a definite physical situation with certain boundary conditions. These conditions are identified for well-known pseudotensors.