Gravitational radiation and holography

This thesis is concerned with the topic of gravitational radiation in asymptotically locally (anti)-de Sitter spacetimes and, in particular, how one can use the tools of holographic duality to provide deeper insights into the nature of radiation. The thesis can broadly be separated into two parts. The first part approaches the topic of gravitational radiation by studying gravity in Bondi-Sachs gauge, specifically solutions to the vacuum Einstein equations Rμ = gμ in the presence of a cosmological constant ̸= 0. We solve these equations for an axisymmetric Bondi-Sachs metric and observe that these differential equa- tions admit an algebraic re-writing based upon data at the conformal boundary, I, of the space-time. Using the Fefferman-Graham coordinate expansion and tools of the AdS/CFT correspondence we are further able to analyse the solutions in the Bondi-Sachs gauge and comment upon the holographic interpretation of the Bondi Sachs data at I. We examine the notion of Bondi mass in AdS and discuss whether or not the natural candidate for such a quantity obeys the monotonicity properties that one would expect due to outgoing gravitational radiation. We finally examine methods of ‘breaking’ the Bondi gauge in order to relax aspects of the gauge which appear overly restrictive. The second part of the thesis turns attention to asymptotically locally dS4 spacetimes ( > 0) and a discussion of how one can apply Bondi-Sachs gauge as well as other techniques in order to gain an understanding of gravitational radiation in this class of spacetimes. We give the analytic continuation of the Fefferman-Graham expansion from Bondi-AdS to Bondi-dS spacetimes as well as an analysis of the asymptotic gravitational charges using the covariant phase space formalism, together with holographic renormalisation techniques adapted to dS spacetime. We provide explicit examples of these charges by considering tensorial perturbations of dS4 in the inflationary patch coordinates, before finally connecting this example to global coordinates via a Bogoliubov transformation of the tensorial mode coefficients