Equations of Motion for Compact Binaries in Einstein-Aether Gravity: A Post-Newtonian Approach

We continue our exploration of the Einstein-Aether(EA) and Khronometric theories of gravity. These theories extend the gravitational theory by adding a long-range vector field to the action. In EA theory, this vector field is constrained to have unit norm. Current observations from binary pulsar and solar system experiments have placed some bounds on the EA parameters. However, the strong-field regime of compact binary systems remains under-explored in the context of EA. Adapting the Direct Integration of the Relaxed Einstein Equations and the post-Minkowskian method to these theories, we have obtained a solution for the metric and the Aether field to 2.5 post-Newtonian order. We use the convention devised by Eardley to treat non-spinning compact bodies as pointlike objects with masses that are sensitive to the vector field.

We report on progress toward obtaining the equations of motion for compact binary systems within Einstein-Aether gravity. This critical step will enable us in future work to predict gravitational waveforms. This will allow researchers at the LIGO-Virgo-Kagra observatories to impose constraints on the theory’s parameter space.