Compact Binary Systems in Einstein-Aether Gravity*

In this work we use the post-Minkowskian approach to analyze the Einstein-Aether(AE)/Khronometric theories of gravity. These theories add a long-range vector field to the spacetime metric. The vector field is constrained to have unit norm in AE theory. This theory has been constrained using solar system and binary pulsar observations, but we want to study strong-field constraints using gravitational waves. We constrain one of the free parameters of the theory to guarantee that light and tensor gravitational waves propagate at the same speed, as seen in the multimessenger event GW170817. This leaves us with a three-parameter subset of the theory. We study the PN expansion of Einstein-Aether gravity using direct integration of the relaxed Einstein equations and we employ the usual conventions for treating non-spinning compact objects whose masses are sensitive to the vector field. We have found a field redefinition that converts the field equations into decoupled, flat-spacetime wave equations for each of the metric and vector perturbation components with right-hand sides that contain matter terms and field terms that are quadratic and higher order in the small perturbations, precisely paralleling the “relaxed Einstein equations” of general relativity. We will report on progress toward obtaining the near-zone metric and the equations of motion for compact binaries to 2.5 PN order.