Energy in the Einstein-Aether Theory
arXiv:gr-qc/0507059 · doi:10.1103/PhysRevD.73.084026 10.1103/PhysRevD.80.129905
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.
10 pages; v2: revised manuscript, final version, to appear in PRD; v3: corrected error in the equation for the aether stress tensor, results unchanged since correct form was used in calculations
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