Probing the non-linear structure of general relativity with black hole binaries

TL;DR

This paper proposes a new method to test the non-linear structure of general relativity by systematically measuring and verifying the consistency of post-Newtonian coefficients in gravitational wave signals from black hole binaries observed by LISA and EGO.

Contribution

It introduces a systematic approach to measure multiple post-Newtonian coefficients independently and test their mutual consistency, improving upon previous methods affected by covariances.

Findings

LISA and EGO can measure post-Newtonian coefficients with high precision.

The method allows testing the self-consistency of all computed post-Newtonian coefficients.

High-accuracy measurements enable stringent tests of general relativity's non-linear structure.

Abstract

Observations of the inspiral of massive binary black holes (BBH) in the Laser Interferometer Space Antenna (LISA) and stellar mass binary black holes in the European Gravitational-Wave Observatory (EGO) offer an unique opportunity to test the non-linear structure of general relativity. For a binary composed of two non-spinning black holes, the non-linear general relativistic effects depend only on the masses of the constituents. In a recent letter, we explored the possibility of a test to determine all the post-Newtonian coefficients in the gravitational wave-phasing. However, mutual covariances dilute the effectiveness of such a test. In this paper, we propose a more powerful test in which the various post-Newtonian coefficients in the gravitational wave phasing are systematically measured by treating three of them as independent parameters and demanding their mutual consistency. LISA (EGO) will observe BBH inspirals with a signal-to-noise ratio of more than 1000 (100) and thereby test the self-consistency of each of the nine post-Newtonian coefficients that have so-far been computed, by measuring the lower order coefficients to a relative accuracy of $\sim 10^{-5}$ (respectively, $\sim 10^{-4}$) and the higher order coefficients to a relative accuracy in the range $10^{-4}$-0.1 (respectively, $10^{-3}$-1).