Compact binary systems in Einstein-Aether gravity: Direct integration of the relaxed field equations to 2.5 post-Newtonian order

Abstract

The Einstein-Aether theory is an alternative theory of gravity in which the spacetime metric is supplemented by a long-range timelike vector field (the "aether" field). Here, for the first time, we apply the full formalism of post-Minkowskian theory and of the Direct Integration of the Relaxed Einstein Equations (DIRE), to this theory of gravity, with the goal of deriving equations of motion and gravitational waveforms for orbiting compact bodies to high orders in a post-Newtonian expansion. Because the aether field is constrained to have unit norm, a naive application of post-Minkowskian theory leads to contributions to the effective energy momentum tensor that are {\em linear} in the perturbative fields. We show that a suitable redefinition of fields using an array of "superpotentials" can eliminate such linear terms to any desired post-Newtonian order, resulting in flat spacetime wave equations for all fields, with sources consisting of matter terms and terms quadratic and higher in the fields. As an initial application of this new method, and as a foundation for obtaining the equations of motion for compact binaries, we obtain explicit solutions of the relaxed equations sufficient to obtain the metric in the near zone through 2.5 post-Newtonian order, or $O[(v/c{)}^5]$ beyond the Newtonian approximation.

17 pages; minor corrections and changes to agree with published version

References in corpus (13)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The Confrontation between General Relativity and Experiment
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Quantum Gravity at a Lifshitz Point
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• The Tensor-Vector-Scalar theory and its cosmology
• Generalizing TeVeS Cosmology
• Compact binary systems in scalar-tensor gravity. III. Scalar waves and energy flux
• Strong field effects on binary systems in Einstein-aether theory
• Motion of Small Bodies in Classical Field Theory

Cited by in corpus (5)

• The Science of the Einstein Telescope
• Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications
• Minimal Einstein-Aether Theory
• Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order
• Eikonal gravitational-wave lensing in Einstein-aether theory