Gravitational Radiation at Infinity with Non-Negative Cosmological Constant

Abstract

The existence of gravitational radiation arriving at null infinity J+, i.e., escaping from the physical system, is addressed in the presence of a non-negative cosmological constant Λ≥0. The case with vanishing Λ is well understood and relies on the properties of the News tensor field (or the News function) defined at J+. The situation is drastically different when Λ>0, where there is no known notion of `News’ with similar good properties. In this paper, both situations are considered jointly from a tidal point of view, that is, taking into account the strength (or energy) of the curvature tensors. The fundamental object used for this purposes is the asymptotic (radiant) super-momentum, a causal vector defined at infinity with remarkable properties. This leads to a novel characterization of gravitational radiation valid for the general case with Λ≥0, which has been proven to be equivalent when Λ=0 to the standard one based on News. Here, the implications of this result when Λ>0 are analyzed in detail. A general procedure to construct `News tensors’ when Λ>0 is depicted, a proposal for asymptotic symmetries is provided, and an example of a conserved charge that may detect gravitational radiation at J+ is exhibited. A series of illustrative examples is listed as well.

Gravitational radiation with Λ>0

“…In other words, based on the super-Poynting vector criterion a spacetime may be labeled as nonradiating, while based on C AB it would be considered radiating. It is therefore not too surprising that the authors in follow-up work found that the asymptotic symmetry algebra for the spacetimes they considered are infinite dimensional [64][65][66].…”

Symplectic charges in the Yang-Mills theory of the normal conformal Cartan connection: applications to gravity

“…The interest in the conformal completions of Einstein spacetimes [1][2][3][4][5][6][7][8] stems from their applications in the analysis of the asymptotics of solutions, as well as the holographic theory. It leads to considerations that use both Einstein's equations and conformal geometry simultaneously.…”