Equations of motion of Compact Binary Systems in Einstein-Aether Gravity*

In this study, we analyze the Einstein-Aether(AE)/Khronometric theories of gravity using the post-Minkowskian approach.These theories extend the spacetime metric by adding a long-range vector field. In AE theory, the vector field is constrained to have a unit norm. Solar system and binary pulsar observations have been used previously to constrain this theory; here we intend to explore strong-field constraints using gravitational waves. To ensure that light and tensor gravitational waves propagate at the same speed as observed in the multimessenger event GW170817, we constrain one of the theory’s free parameters. This leaves us with a three-parameter subset of the theory. We adapt the formalism of the Direct Integration of the Relaxed Einstein Equations to these theories and obtain the post-Newtonian (PN) expansion of the fields to 2.5 PN order. We use the convention devised by Eardley to treat non-spinning compact objects with masses that are sensitive to the vector field. We have generalized the Eardley approach to a wide class of alternative theories of gravity with a range of scalar, vector and tensor auxiliary field couplings to the masses. We will report on progress toward obtaining the near-zone metric and the equations of motion for compact binaries to 2.5 PN order.