Gravitational radiation in full general relativity with a non-negative cosmological constant

ABSTRACT:

A covariant, gauge-invariant criterion for the existence, or absence, of gravitational radiation at infinity with non-negative cosmological constant (Lambda) is presented. For Lambda>0, the fundamental idea is that the physical asymptotic properties are encoded in {I,h,D}, where I is a three-dimensional manifold, h is a representative of a conformal class of Riemannian metrics on I, and D is a rank-2, traceless, symmetric tensor field on I.

Based on this, and on the tidal nature of gravitational radiation, a characterisation of gravitational radiation at the conformal boundary is given using the asymptotic properties of the rescaled Bel-Robinson tensor. The asymptotically flat scenario is also reviewed. In this case, the new criterion is shown to be fully equivalent to the classical one based on the news tensor. Also, a new balance law at infinity is presented. (Based on joint work with José M. M. Senovilla)