  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.

High Energy Physics - Theory;General Relativity and Quantum Cosmology