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The Laser Interferometer Gravitational-Wave Observatory (LIGO) has recentlydiscovered gravitational waves (GWs) from its first neutron star-neutron starmerger at a distance of $\sim 40$~Mpc from the Earth. The associatedelectromagnetic (EM) detection of the event, including the short gamma-rayburst within $\Delta t \sim 2$~s after the GW arrival, can be used to testvarious aspects of sources physics and GW propagation. Using GW170817 as thefirst GW-EM example, we show that this event provides a stringent direct testthat GWs travel at the speed of light. The gravitational potential of the MilkyWay provides a potential source of Shapiro time delay difference between thearrival of photons and GWs, and we demonstrate that the nearly coincidentdetection of the GW and EM signals can yield strong limits on anomalousgravitational time delay, through updating the previous limits taking intoaccount details of Milky Way's gravitational potential. Finally, we also obtainan intriguing limit on the size of the prompt emission region of GRB 170817A,and discuss implications for the emission mechanism of short gamma-ray bursts.

Constraints from the Time Lag between Gravitational Waves and Gamma Rays: Implications of GW 170817 and GRB 170817A