Gravitational-wave generation in the presence of Lorentz invariance violation

TL;DR

This paper develops a method to analyze gravitational waves in a Lorentz invariance violating extension of General Relativity, providing a foundation for future experimental tests with detectors like LISA.

Contribution

It derives and solves the gravitational wave equation within a Lorentz-violating framework using the MPM method, linking theoretical modifications to observable waveforms.

Findings

Derived the modified wave equation for gravitational waves with Lorentz violation.

Solved the wave equation using the MPM method for the SME extension.

Outlined how these results can help constrain Lorentz invariance violations with future detectors.

Abstract

We solve the wave equation for gravitational waves emitted by compact objects systems using the Multipolar Post-Minkowskian (MPM) method, and in the presence of Lorentz invariance violating terms. We select a Lorentz-violating extension of General Relativity in the pure gravity sector, directly taken from the Standard Model Extension (SME) formalism, and derive the wave equation for metric perturbation from the modified Einstein equation. We solve it with the MPM method and compute the gauge-invariant Riemann tensor components governing the geodesic deviation. Finally we compare the leading order term of the perturbative scheme in the small SME coefficients, with the leading order of the General Relativity. We outline the benefits and difficulties of this method. All the results are given as functionals of a set of general PM moments that can be matched to the physical properties of the source. These results are a first step toward putting state-of-the-art constraints on symmetries violations with new gravitational wave detectors like LISA.