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The coincident detection of a gravitational-wave (GW) event GW170817 withelectromagnetic (EM) signals (e.g., a short gamma-ray burst SGRB 170817A or amacronova) from a binary neutron star merger within the nearby galaxy NGC 4933provides a new, multimessenger test of the weak equivalence principle (WEP),extending the WEP test with GWs and photons. Assuming that the arrival timedelay between the GW signals from GW170817 and the photons from SGRB 170817A orthe macronova is mainly attributed to the gravitational potential of the MilkyWay, we demonstrate that the strict upper limits on the deviation from the WEPare $\Delta \gamma<1.4\times10^{-3}$ for GW170817/macronova and $\Delta \gamma<5.9\times10^{-8}$ for GW170817/SGRB 170817A. A much more severe constraint onthe WEP accuracy can be achieved ($\sim0.9\times10^{-10}$) for GW170817/SGRB170817A when we consider the gravitational potential of the Virgo Cluster,rather than the Milky Way's gravity. This provides the tightest limit to dateon the WEP through the relative differential variations of the $\gamma$parameter for two different species of particles. Compared with othermultimessenger (photons and neutrinos) results, our limit is 7 orders ofmagnitude tighter than that placed by the neutrinos and photons from supernova1987A, and is almost as good as or is an improvement of 6 orders of magnitudeover the limits obtained by the low-significance neutrinos correlated with GRBsand a blazar flare.

Multimessenger tests of the weak equivalence principle from GW170817 and its electromagnetic counterparts