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

Abstract

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. This provides in particular a new derivation of the (A)dS mass loss formula. We then study the holographic renormalisation of the symplectic potential, and the transformation laws under residual asymptotic symmetries. The advantage of the partial Bondi gauge is that it allows to contrast and treat in a unified manner the Bondi-Sachs and Newman-Unti gauges, which can each be reached upon imposing a further specific gauge condition. The differential determinant condition leads to the Λ-BMSW gauge, while a differential condition on g ur leads to a generalized Newman-Unti gauge. This latter gives access to a new asymptotic symmetry which acts on the asymptotic shear and further extends the Λ-BMSW group by an extra abelian radial translation. This generalizes results which we have recently obtained in three dimensions.

Gravitational memory effects and higher derivative actions

“…For example, the standard displacement memory effect [19,20,29] is related to supertranslation charges [3,5]. Given the plethora of memory effects [4,14,[30][31][32][33][34][35] and various extensions of the asymptotic symmetry group [12,13,[16][17][18][36][37][38][39][40], a natural programme to consider is one of relating the various memory effects to the various asymptotic charges, in the hope that one may learn something new about semi-classical/quantum gravity.…”

“…One possible explanation for the relation of these memory effects to internal Lorentz charges is that beyond the standard and dual BMS charges derived from the two-derivatve terms in the action, there are no other independent charges and that the internal charges conveniently repackage an expression that may equally be interpreted as a spacetime rotation or even superrotation charge [12]. Another possibility is that the internal Lorentz charges are in fact related to various extensions of the BMS group [13,17,18,39,40,66]. In order to investigate this, one must first investigate the charges associated with the additional symmetry generators.…”