On the canonical energy of weak gravitational fields with a cosmological constant Lambda is an element of R

Abstract

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 Lambda >0 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 Chruciel and Ifsits (Phys Rev D 93:124075, arXiv:1603.07018 [gr-qc], 2016).

Keywords

• yano-killing tensors
• general-relativity
• initial data
• space-times
• equations
• einstein
• existence
• gravity
• waves