The Weyl BMS group and Einstein's equations
Abstract
We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes supertranslations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the BarnichTroessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the fluxbalance laws for the Noether charges imply the validity of the asymptotic Einstein's equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2021
 DOI:
 10.1007/JHEP07(2021)170
 arXiv:
 arXiv:2104.05793
 Bibcode:
 2021JHEP...07..170F
 Keywords:

 Models of Quantum Gravity;
 SpaceTime Symmetries;
 Classical Theories of Gravity;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 53 pages + appendix, 1 figure