Gravitational radiation at infinity with negative cosmological constant and AdS$_4$ holography

TL;DR

This paper develops a covariant framework to characterize gravitational radiation at infinity in asymptotically AdS spacetimes with negative cosmological constant, linking boundary data and geometric properties of the Weyl tensor.

Contribution

It introduces a new covariant characterization of gravitational radiation at infinity in AdS$_4$, including boundary conditions that determine the presence or absence of radiation.

Findings

Boundary conditions for no radiation derived

Covariant criteria based on Weyl tensor properties established

Conditions for excluding incoming or outgoing radiation identified

Abstract

The covariant characterization of the existence of gravitational radiation traversing infinity $\mathscr{J}$ in the presence of a negative cosmological constant is presented. It is coherent and consistent with the previous characterizations put forward for the cases of non-negative cosmological constant, relying on the properties of the asymptotic super-Poynting vector; or in more transparent terms, based on the intrinsic properties of the flux of tidal energy at infinity. The proposed characterization is fully satisfactory, it can be covariantly typified in terms of boundary data at infinity, and it can also be categorized according to the geometric properties of the rescaled Weyl tensor at $\mathscr{J}$. The cases with no incoming radiation entering from (or no outgoing radiation escaping at) $\mathscr{J}$ can similarly be determined in terms of the boundary data or geometric properties of the rescaled Weyl tensor. In particular, we identify the most general boundary conditions that, in an initial-boundary value problem, ensure absence of gravitational radiation traversing $\mathscr{J}$, namely (functional) proportionality between the Cotton-York tensor field and the holographic stress tensor field at $\mathscr{J}$. We also present novel conditions ensuring the absence of just incoming (outgoing) radiation at $\mathscr{J}$. These are given in a covariant way and also in terms of standard rescaled Weyl tensor scalars. The results are compatible with any matter content of the physical spacetime.