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

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.

arXiv comment70 pages, 11 figures, Mathematica file with the solutions to the Einstein equations and the transformation from Bondi to Fefferman-Graham gauges attached. v2: Accepted for publication in Classical and Quantum Gravity, appendix added providing a comparison of Bondi and Abbott-Deser masses, references added

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Cited by in corpus (39)

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• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
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• Holographic Lorentz and Carroll Frames
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• Nonperfect Carrollian Fluids Through Holography