Testing general relativity with compact-body orbits: A modified Einstein-Infeld-Hoffmann framework

Abstract

We describe a general framework for analyzing orbits of systems containing compact objects (neutron stars or black holes) in a class of Lagrangian-based alternative theories of gravity that also admit a global preferred reference frame. The framework is based on a modified Einstein-Infeld-Hoffmann (EIH) formalism developed by Eardley and by Will, generalized to include the possibility of Lorentz-violating, preferred-frame effects. It uses a post-Newtonian $N$-body Lagrangian with arbitrary parameters that depend on the theory of gravity and on "sensitivities" that encode the effects of the bodies' internal structure on their motion. We determine the modified EIH parameters for the Einstein-{\AE}ther and Khronometric vector-tensor theories of gravity. We find the effects of motion relative to a preferred universal frame on the orbital parameters of binary systems containing neutron stars, such as a class of ultra-circular pulsar-white dwarf binaries, the amplitudes of the effects depend upon "strong-field" preferred-frame parameters $\hat{\,\,\alpha}_1$ and ${\hat{\,\,\alpha}}_2$, which we relate to the fundamental modified EIH parameters. We also determine the amplitude of the "Nordtvedt effect" in a triple system containing the pulsar J0337+1715 in terms of the modified EIH parameters.