Energy in the Einstein-Aether Theory

TL;DR

This paper analyzes the energy properties of Einstein-Aether theory, deriving expressions for wave mode energies and total energy in asymptotically flat spacetimes, and discusses energy positivity constraints.

Contribution

It provides the first detailed energy density expressions for wave modes and total energy in Einstein-Aether theory, including linear and non-linear regimes.

Findings

Wave modes have positive energy constraints.

Total energy expression is modified by the aether field.

Non-linear energy positivity remains unresolved.

Abstract

We investigate the energy of a theory with a unit vector field (the "aether") coupled to gravity. Both the Weinberg and Einstein type energy-momentum pseudotensors are employed. In the linearized theory we find expressions for the energy density of the 5 wave modes. The requirement that the modes have positive energy is then used to constrain the theory. In the fully non-linear theory we compute the total energy of an asymptotically flat spacetime. The resulting energy expression is modified by the presence of the aether due to the non-zero value of the unit vector at infinity and its 1/r falloff. The question of non-linear energy positivity is also discussed, but not resolved.