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

TL;DR

This paper develops a generalized framework based on a modified Einstein-Infeld-Hoffmann formalism to analyze the orbital dynamics of compact-body systems in alternative gravity theories that include preferred-frame effects, with applications to pulsar binaries.

Contribution

It introduces a generalized post-Newtonian Lagrangian framework for alternative gravity theories with preferred frames, including explicit parameters for strong-field effects.

Findings

Derived modified EIH parameters for Einstein-{\

Determined effects of preferred-frame motion on binary pulsar orbits.

Quantified the Nordtvedt effect amplitude in a triple pulsar system.

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.