SciPost Phys. 13, 108 (2022) ·
published 15 November 2022
|
· pdf
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 $\Lambda$-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 $\Lambda$-BMSW group by an extra abelian radial translation. This generalizes results which we have recently obtained in three dimensions.
SciPost Phys. 12, 032 (2022) ·
published 21 January 2022
|
· pdf
Generalized dilaton gravity in 2d is the most general consistent deformation
of the Jackiw-Teitelboim model that maintains local Lorentz invariance. The
action is generically not power-counting renormalizable, thus going beyond the
class of models typically studied. Nevertheless, all these models are exactly
soluble. We focus on a subclass of dilaton scale invariant models. Within this
subclass, we identify a 3-parameter family of models that describe black holes
asymptoting to AdS2 in the UV and to dS2 in the IR. Since these models could be
interesting for holography, we address thermodynamics and boundary issues,
including boundary charges, asymptotic symmetries and holographic
renormalization.
