Energy of gravitational radiation in the de Sitter universe at the scri and at a horizon

Abstract

In this note we investigate outcomes of a symplectic formula for the gravitational waves charges in the general relativity linearized around the de Sitter spacetime. We derive their explicit form at {\it scri} in the Bondi frame, compare with the connected Noether expression and analyze their gauge dependence which allows us to fix unambiguously boundary terms. We also discuss minimal requirements needed to impose on initial data to have finite values of charges. Furthermore, we analyze transformation laws of the energy upon the action of the de Sitter group and discuss its physical interpretation. Finally, we calculate its flux through a cosmological horizon instead of {\it scri}. We show that in the limit $\Lambda \to 0$, one recovers Trautman--Bondi formula strengthening recent proposal that one should choose a~null surface as a more natural boundary for the astrophysical systems in the presence of the cosmological constant.

arXiv comment30 pages

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• Charges, conserved quantities and fluxes in de Sitter spacetime
• Analysis of gravitational radiation generated by type D black holes with positive cosmological constant
• On the canonical energy of weak gravitational fields with a cosmological constant $\Lambda \in \mathbb{R}$
• A generalization of the quadruple formula for the energy of gravitational radiation in de Sitter spacetime
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• Symmetries of the asymptotically de Sitter spacetimes
• Charged Taub-NUT-de Sitter spacetime in DGP braneworld and its thermodynamics
• The Kerr-de Sitter spacetime in Bondi coordinates