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}grr=0=grA 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 \LambdaΛ-BMSW gauge, while a differential condition on g_{ur}gur 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 \LambdaΛ-BMSW group by an extra abelian radial translation. This generalizes results which we have recently obtained in three dimensions.

Electrodynamics under the action of null cosmic strings

“…Their key property is in non-analytical behavior at conformal null infinities, see e.g. [29,30,31,32,33,34]. The logarithmic terms result in the corresponding modification of the peeling properties of the curvature invariants [24].…”

“…The differences between (4.2) and asymptotic (4.12) are the following: i) we admit possibility of higher order powers of the logarithms [29,30,31,32,33,34], ii) we do not require that amplitudes H(2) , Q(2) are static. Also note that conditions (4.4), (4.5) are not to be applicable to H (2) , H(2) , Q(2) .…”

The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher $$\ell $$-Modes of Linear Waves on a Schwarzschild Background

“…That some weakening of this kind should be done was already suggested in [Sac62b], Page 110. We also refer to [GZ22], where a partial Bondi gauge is studied, and where b in (1.34) is not assumed to vanish (but b ′ in (1.35) is).…”

Radiative asymptotic symmetries of 3D Einstein-Maxwell theory

“…Radiative asymptotic symmetries are thus crucial for quantum gravity and gauge theories as a whole, and for Minkowskian holography in particular [13,[32][33][34][35][36][37][38][39]. Note that similar questions can also be raised in (Anti)-de Sitter [(A)dS] spacetimes, where radiation and holography with porous boundary conditions were recently studied in [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57].…”

“…Actually, an analogous situations occurs in 4D pure gravity, where one can relax boundary conditions so that the solution space contains other undetermined functions of u on top of the two degrees of freedom in the asymptotic shear C ab . This includes for instance the induced boundary metric on + [53,54] or the trace of C ab in Newman-Unti gauge [54,92], and it allows one to describe physically relevant solutions with C ab = 0, such as Robinson-Trautman spacetimes [93][94][95]. The metric on + can similarly be relaxed in 3D pure gravity, resulting in a phase space with three unspecified functions of u even though the bulk theory has no propagating degrees of freedom at all [96,97].…”