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The discovery of gravitational waves (GWs) provides an unprecedented arena totest general relativity, including the gravitational Lorentz invarianceviolation (gLIV). In the propagation of GWs, a generic gLIV leads toanisotropy, dispersion, and birefringence. GW events constrain the anisotropicbirefringence particularly well. Kosteleck\'y and Mewes (2016) performed apreliminary analysis for GW150914. We improve their method and extend theanalysis systematically to the whole GW transient catalog, GWTC-1. This is thefirst global analysis of the spacetime anisotropic Lorentzian structure with acatalog of GWs, where multiple events are crucial in breaking the degeneracyamong gLIV parameters. With the absence of abnormal propagation, we obtain newlimits on 34 coefficients for gLIV in the nonminimal gravity that surpassprevious limits by $\sim 10^2$-$10^5$.

Combined search for anisotropic birefringence in the gravitational-wave transient catalog GWTC-1