Testing the speed of gravitational waves over cosmological distances with strong gravitational lensing

Probing the relative speeds of gravitational waves and light acts as an important test of General Relativity and alternative theories of gravity. Measuring the arrival time of gravitational waves and electromagnetic counterparts can be used to measure the relative speeds, but only if the intrinsic time-lag between emission of the photons and gravitational waves is well understood. Here we suggest a method that does not make such an assumption, using future strongly lensed GW events and EM counterparts; Biesiada et al forecast that 50-100 strongly lensed GW events will be observed each year with the Einstein Telescope. A single strongly lensed GW event would produce robust constraints on the ratio of speeds of GWs and light at the $10^{-7}$ level, if a high energy EM counterpart is observed within the field-of-view of an observing gamma ray burst monitor.