Testing general relativity via direct measurement of black hole kicks

TL;DR

This paper explores the potential to directly measure black hole recoil velocities caused by asymmetric gravitational wave emission during mergers, enabling tests of general relativity through gravitational wave observations.

Contribution

It introduces a method to measure black hole kicks from gravitational wave data and proposes a new test of general relativity based on linear momentum conservation.

Findings

Future detectors can measure black hole kicks with 2-30% accuracy.

Certain binary configurations allow sub-percent-level kick measurements.

The proposed null variable test can constrain deviations from general relativity to 3-30%.

Abstract

Asymmetric emission of gravitational waves during a compact binary coalescence results in the loss of linear momentum and a corresponding "kick" or recoil on the binary's center of mass. This leads to a direction-dependent Doppler shift of the ringdown gravitational waveform. We quantify the measurability of the kick imparted to the remnant black hole in a binary black hole merger. Future ground- and space-based gravitational-wave detectors will measure this effect to within $\sim 2\%$ to $\sim 30\%$ for a subset of their expected observed sources. Certain binary configurations in the LISA band may allow a sub-percent-level measurement of this effect. This direct measurement of black hole kicks can also facilitate a novel test of general relativity based on linear momentum balance. We formulate this kick consistency test via measurement of a null variable that quantifies the difference between the inferred kick (using numerical relativity) and that observed via the Doppler-shifted ringdown signal. This null variable can be constrained (at 90\% confidence) to $\sim 10\%$ to $30\%$ with Cosmic Explorer and to $\sim 3\%$ to $12\%$ with LISA.