Speed of Gravitational Waves from Strongly Lensed Gravitational Waves and Electromagnetic Signals

TL;DR

This paper introduces a model-independent method to measure the speed of gravitational waves using strongly lensed GW-EM events, which is robust against lens modeling and internal delays, and is feasible with upcoming third-generation detectors.

Contribution

It proposes a novel, theory-agnostic approach to determine GW propagation speed through differential time delay measurements in lensed GW-EM signals.

Findings

Method is robust against lens modeling uncertainties.

Timing accuracy can be improved by identifying short transients.

Expected to be feasible with future third-generation GW detectors.

Abstract

We propose a new model-independent measurement strategy for the propagation speed of gravitational waves (GWs) based on strongly lensed GWs and their electromagnetic (EM) counterparts. This can be done in two ways: by comparing arrival times of GWs and their EM counterparts and by comparing the time delays between images seen in GWs and their EM counterparts. The lensed GW-EM event is perhaps the best way to identify an EM counterpart. Conceptually, this method does not rely on any specific theory of massive gravitons or modified gravity. Its differential setting (i.e., measuring the difference between time delays in GW and EM domains) makes it robust against lens modeling details (photons and GWs travel in the same lensing potential) and against internal time delays between GW and EM emission acts. It requires, however, that the theory of gravity is metric and predicts gravitational lensing similar to general relativity. We expect that such a test will become possible in the era of third-generation gravitational-wave detectors, when about 10 lensed GW events would be observed each year. The power of this method is mainly limited by the timing accuracy of the EM counterpart, which for kilonovae is around $10^4$ s.Thisuncertaintycanbesuppressedbya factor of $\sim 10^{10}$, if strongly lensed transients of much shorter duration associated with the GW event can be identified. Candidates for such short transients include short gamma-ray burst and fast radio bursts.