(A)dS$\mathbf{_4}$ in Bondi gauge

TL;DR

This paper derives the most general asymptotic solutions of Einstein gravity in Bondi gauge for both flat and (A)dS spacetimes, providing new integration schemes and insights into holographic data extraction.

Contribution

It presents the first comprehensive derivation of asymptotic solutions in Bondi gauge for Einstein gravity with a cosmological constant, including explicit transformation to Fefferman-Graham gauge.

Findings

Bondi mass remains constant in asymptotically AdS4 spacetimes

New integration schemes for non-zero cosmological constant cases

Explicit methods for extracting holographic data from Bondi coordinates

Abstract

We obtain the general asymptotic solutions of Einstein gravity with or without cosmological constant in Bondi gauge. The Bondi gauge was originally introduced in the context of gravitational radiation in asymptotically flat gravity. In the original work, initial conditions were prescribed at a null hypersurface and the Einstein equations were shown to take a nested form, which may be used to explicitly integrate them asymptotically. We streamline the derivation of the general asymptotic solution in the asymptotically flat case, and derive the most general asymptotic solutions for the case of non-zero cosmological constant of either sign (asymptotically locally AdS and dS solutions). With non-zero cosmological constant, we present integration schemes which rely on either prescribing data on the conformal boundary or on a null hypersurface and part of the conformal boundary. We explicitly work out the transformation to Fefferman-Graham gauge and identity how to extract the holographic data directly in Bondi coordinates. We illustrate the discussion with a number of examples and show that for asymptotically AdS${}_4$ spacetimes the Bondi mass is constant.