Abstract
The asymptotic symmetry group of general relativity in asymptotically flat spacetimes can be extended from the Bondi-Metzner-Sachs (BMS) group to the generalized BMS (GMBS) group suggested by Campiglia and Laddha, which includes arbitrary diffeomorphisms of the celestial two-sphere. It can be further extended to the Weyl BMS (BMSW) group suggested by Freidel, Oliveri, Pranzetti and Speziale, which includes general conformal transformations. We compute the action of fully nonlinear BMSW transformations on the leading order Bondi-gauge metric functions: specifically, the induced metric, Bondi mass aspect, angular momentum aspect, and shear. These results generalize previous linearized results in the BMSW context by Freidel et al., and also nonlinear results in the BMS context by Chen, Wang, Wang and Yau. The transformation laws will be useful for exploring implications of the BMSW group.
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Acknowledgments
We thank Bob Wald for a helpful conversation and for pointing out to us the reference [16]. E.E.F. was supported in part by NSF grant PHY-2110463 and by a Simons Foundation Fellowship. D.A.N. acknowledges support from NSF Grants No. PHY-2011784 and No. PHY-2309021.
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Flanagan, É.É., Nichols, D.A. Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group. J. High Energ. Phys. 2024, 120 (2024). https://doi.org/10.1007/JHEP03(2024)120
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DOI: https://doi.org/10.1007/JHEP03(2024)120