Energy and momentum in multiple metric theories

TL;DR

This paper derives expressions for energy, momentum, and angular momentum in multi-metric theories, proving total energy conservation as a sum of individual metrics' energies and establishing a positive energy theorem.

Contribution

It introduces a Hamiltonian formalism for a subset of multi-metric theories and demonstrates that total energy is conserved and positive despite metric interactions.

Findings

Total energy equals the sum of energies from each metric.

A positive energy theorem is established.

A Hamiltonian formalism for multi-metric theories is presented.

Abstract

We derive the expressions for canonical energy, momentum, and angular momentum for multiple metric theories. We prove that although the metric fields are generally interacting, the total energy is the sum of conserved energies corresponding to each metric. A positive energy theorem is given as a result. In addition, we present an Hamiltonian formalism for a subgroup of multi-metric theories.