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

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.

15 pages, no figures

References in corpus (11)

• Asymptotic symmetries and subleading soft graviton theorem
• New symmetries for the Gravitational S-matrix
• The Weyl BMS group and Einstein's equations
• Sub-subleading soft gravitons and large diffeomorphisms
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• A general framework for gravitational charges and holographic renormalization
• Gravity from symmetry: Duality and impulsive waves
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Extensions of the asymptotic symmetry algebra of general relativity
• Geometric action for extended Bondi-Metzner-Sachs group in four dimensions
• Infrared Effects in the Late Stages of Black Hole Evaporation

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