Angular Momentum Loss for a Binary System in Einstein-{\AE}ther Theory

TL;DR

This paper calculates the angular momentum and energy decay rates of binary systems in Einstein-e7her theory, showing they are faster than in General Relativity, which could help test the theory with gravitational wave data.

Contribution

It provides the first detailed computation of angular momentum loss in Einstein-e7her theory for binary inspirals, linking it to observable gravitational wave signatures.

Findings

Angular momentum decay is faster in Einstein-e7her theory than in GR.

Dipole radiation significantly influences the orbital decay rates.

Potential gravitational wave signatures could constrain Einstein-e7her theory.

Abstract

The recent gravitational wave observations provide insight into the extreme gravity regime of coalescing binaries, where gravity is strong, dynamical and non-linear. The interpretation of these observations relies on the comparison of the data to a gravitational wave model, which in turn depends on the orbital evolution of the binary, and in particular on its orbital energy and angular momentum decay. In this paper, we calculate the latter in the inspiral of a non-spinning compact binary system within Einstein-\AE{}ther theory. From the theory's gravitational wave stress energy tensor and a balance law, we compute the angular momentum decay both as a function of the fields in the theory and as a function of the multipole moments of the binary. We then specialize to a Keplerian parameterization of the orbit to express the angular momentum decay as a function of the binary's orbital elements. We conclude by combining this with the orbital energy decay to find expressions for the decay of the semi-major axis and the orbital eccentricity of the binary. We find that these rates of decay are typically faster in Einstein-\AE{}ther theory than in General Relativity due to the presence of dipole radiation. Such modifications will imprint onto the chirp rate of gravitational waves, leaving a signature of Einstein-\AE{}ther theory that if absent in the data could be used to stringently constrain it.