Gravitational charges and radiation in asymptotically locally de Sitter spacetimes

TL;DR

This paper develops a formalism for defining and analyzing gravitational charges and radiation in four-dimensional asymptotically locally de Sitter spacetimes, highlighting conditions for conservation and flux laws.

Contribution

It introduces a well-posed variational principle with boundary terms, and derives conserved and flux-balance laws for gravitational charges in AldS spacetimes.

Findings

Conserved charges are associated with asymptotic conformal Killing vectors.

Flux-balance laws govern the evolution of gravitational charges.

Existence of monotonic charges like the Bondi mass in AldS spacetimes.

Abstract

We present a comprehensive discussion of gravitational charges and radiation in four-dimensional asymptotically locally de Sitter (AldS) spacetimes. Such spacetimes have compact spatial sections and possess spacelike past and future infinities, $\mathscr{I}^\pm$. We show that the variational problem is well-posed if one specifies a conformal class up to three-dimensional diffeomorpshims at $\mathscr{I}^\pm$, provided one adds at $\mathscr{I}^\pm$ suitable local terms. These are analogues of the AdS covariant counterterms of holographic renormalisation. Radiation is possible only when the conformal class at infinity is non-trivial. Bulk diffeomorphisms that asymptote to conformal Killing vectors at $\mathscr{I}^\pm$ lead to gravitational charges that are conserved under radial translations, while transformations that asymptote to a general three-dimensional vector imply that the gravitational charges satisfy flux-balance laws. We also present quantities that are invariant under temporal translations, if gravitational flux is absent, but otherwise satisfy flux-balance laws. We derive these results using first principles application of Noether's method as well as covariant phase space methods. We apply our formalism to several exact solutions, including the Robinson-Trautman-dS class, which we use to demonstrate the existence of conserved charges even in the absence of asymptotic conformal Killing vectors and the existence of monotonic charges, including the Bondi mass.