SciPost Phys. 13, 108 (2022) ·
published 15 November 2022

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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 socalled 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, timedependent 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 NewmanPenrose 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 NewmanUnti 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 NewmanUnti 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. 10, 022 (2021) ·
published 29 January 2021

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We reveal an $\mathfrak{iso}(2,1)$ Poincar\'e algebra of conserved charges
associated with the dynamics of the interior of black holes. The action of
these Noether charges integrates to a symmetry of the gravitational system
under the Poincar\'e group ISO$(2,1)$, which allows to describe the evolution
of the geometry inside the black hole in terms of geodesics and horocycles of
AdS${}_2$. At the Lagrangian level, this symmetry corresponds to M\"obius
transformations of the proper time together with translations. Remarkably, this
is a physical symmetry changing the state of the system, which also naturally
forms a subgroup of the much larger
$\textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)$ group, where
$S^1$ is the compactified time axis. It is intriguing to discover this
structure for the black hole interior, and this hints at a fundamental role of
BMS symmetry for black hole physics. The existence of this symmetry provides a
powerful criterion to discriminate between different regularization and
quantization schemes. Following loop quantum cosmology, we identify a
regularized set of variables and Hamiltonian for the black hole interior, which
allows to resolve the singularity in a blacktowhite hole transition while
preserving the Poincar\'e symmetry on phase space. This unravels new aspects of
symmetry for black holes, and opens the way towards a rigorous group
quantization of the interior.
Dr Geiller: "1. It is correct that the Weyl..."
in Submissions  report on The partial Bondi gauge: Further enlarging the asymptotic structure of gravity