Testing Einstein's Weak Equivalence Principle With Gravitational Waves
  A conservative constraint on the Einstein Weak Equivalence Principle (WEP) can be obtained under the assumption that the observed time delay between correlated particles from astronomical sources is dominated by the gravitational fields through which they move. Current limits on the WEP are mainly based on the observed time delays of photons with different energies. It is highly desirable to develop more accurate tests that include the gravitational wave (GW) sector. The detection by the advanced LIGO/VIRGO systems of gravitational waves will provide attractive candidates for constraining the WEP, extending the tests to gravitational interactions, with potentially higher accuracy. Considering the capabilities of the advanced LIGO/VIRGO network and the source direction uncertainty, we show that the joint detection of GWs and electromagnetic signals could probe the WEP to an accuracy down to $10^{-10}$, which is one order of magnitude tighter than previous limits, and seven orders of magnitude tighter than the multi-messenger (photons and neutrinos) results by supernova 1987A. 
Xue-Feng Wu, He Gao, Jun-Jie Wei, Xi-Long Fan, Peter M\'esz\'aros,   Bing Zhang, Zi-Gao Dai, Shuang-Nan Zhang and Zong-Hong Zhu
astro-ph.HE gr-qc hep-ph