The partial Bondi gauge: Further enlarging the asymptotic structure of gravity

Understand

We present a detailed analysis of gravity in a partial Bondi gauge, where only the three conditions $g_{rr}=0=g_{rA}$ are fixed.

• We relax in particular the so-called determinant condition on the transverse metric, which is only assumed to admit a polyhomogeneous radial expansion.
• This is sufficient in order to build the solution space, which here includes a cosmological constant, time-dependent sources in the boundary metric, logarithmic branches, and an extra trace mode at subleading order in the transverse metric.
• The evolution equations are studied using the Newman-Penrose formalism in terms of covariant functionals identified from the Weyl scalars, and we build the explicit dictionary between this formalism and the tensorial Einstein equations.