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 varLambda >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 Chruściel and Ifsits (Phys Rev D 93:124075, arXiv:1603.07018 [gr-qc], 2016).
Highlights
A question of current interest is the amount of energy that can be radiated by a gravitating system in the presence of a positive cosmological constant
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 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 Chrusciel and Ifsits (Phys Rev D 93:124075, arXiv:1603.07018 [gr-qc], 2016)
Summary
A question of current interest is the amount of energy that can be radiated by a gravitating system in the presence of a positive cosmological constant. 3 we show how to put a linearised gravitational field into Bondi gauge, analyse the small-r behaviour of the fields and derive the freedom remaining This gives a unified treatment for all Λ ∈ R of asymptotic symmetries à la Bondi-Metzner-Sachs in the linearised regime, which leads to a clear view of the differences arising from the sign of the cosmological constant and from the boundary conditions imposed. Our asymptotic conditions on the linearised perturbations of the metric are modelled on the asymptotic behaviour of the full solutions of the Einstein vacuum field equations with positive cosmological constant and with smooth initial Cauchy data on S3, as derived by Friedrich in [29]. In [29] Friedrich shows that small perturbations of de Sitter Cauchy data on S3 lead to vacuum spacetimes with smooth conformal boundaries at infinity.
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