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The asymptotic symmetry group of general relativity in asymptotically flatspacetimes can be extended from the Bondi-Metzner-Sachs (BMS) group to thegeneralized BMS (GMBS) group suggested by Campiglia and Laddha, which includesarbitrary diffeomorphisms of the celestial two-sphere. It can be furtherextended to the Weyl BMS (BMSW) group suggested by Freidel, Oliveri, Pranzettiand Speziale, which includes general conformal transformations. We compute theaction of fully nonlinear BMSW transformations on the leading order Bondi-gaugemetric functions: specifically, the induced metric, Bondi mass aspect, angularmomentum aspect, and shear. These results generalize previous linearizedresults in the BMSW context by Freidel et al., and also nonlinear results inthe BMS context by Chen, Wang, Wang and Yau. The transformation laws will beuseful for exploring implications of the BMSW group.

Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group