Regular Article - Theoretical Physics
On the canonical energy of weak gravitational fields with a cosmological constant
1 University of Vienna, Gravitational Physics, Boltzmanngasse, 5, A1090, Wien, Austria
2 Institut de Hautes Études Scientifiques, Le Bois-Marie, 35 rte de Chartres, 91440, Bures-sur-Yvette, France
3 Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00, Prague 8, Czech Republic
4 Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warszawa, Poland
Accepted: 12 June 2021
Published online: 5 August 2021
We analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When the energy diverges, but a renormalised formula with well defined flux is obtained. We show that the renormalised energy in the asymptotically off-diagonal gauge coincides with the quadratisation of the generalisation of the Trautman–Bondi mass proposed in Chruściel and Ifsits (Phys Rev D 93:124075, arXiv:1603.07018 [gr-qc], 2016).
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