Gauges in three-dimensional gravity and holographic fluids

Abstract

Solutions to Einstein’s vacuum equations in three dimensions are locally maximally symmetric. They are distinguished by their global properties and their investigation often requires a choice of gauge. Although analyses of this sort have been performed abundantly, several relevant questions remain. These questions include the interplay between the standard Bondi gauge and the Eddington-Finkelstein type of gauge used in the fluid/gravity holographic reconstruction of these spacetimes, as well as the Fefferman-Graham gauge, when available i.e. in anti de Sitter. The goal of the present work is to set up a thorough dictionary for the available descriptions with emphasis on the relativistic or Carrollian holographic fluids, which portray the bulk from the boundary in anti-de Sitter or flat instances. A complete presentation of residual diffeomorphisms with a preliminary study of their algebra accompanies the situations addressed here.

Conservation and integrability in lower-dimensional gravity

“…Our analysis provides some new results concerning the quest of the most general boundary conditions in two dimensions for a generic class of models that contains JT [82,83] and CGHS [84] gravity theories. Indeed, as suggested in [67,68] (see also [25,42,43]), fixing the gauge completely in the analysis of asymptotics seems to eliminate some potentially interesting asymptotic symmetries and associated towers of charges. In this work, we construct the maximal asymptotic symmetry algebra that one can obtain in two-dimensional gravity theories by imposing only partial gauge fixing on the components of the metric and very mild falloffs.…”

“…In three dimensions, the rigidity of the Bondi gauge fixing does not allow us to pretend for the most general boundary conditions [42,43]. However, our analysis investigates new boundary conditions that encompass those considered previously in the literature (see e.g.…”

“…Furthermore, this set-up is sufficient to illustrate our techniques on renormalization and integrability of non-conserved charges. After performing the holographic renormalization of the action and the symplectic structure in Bondi gauge using covariant counter-terms [27,53,85,86,98] and corner terms [26,98], we obtain the gravitational charges associated with the solution space derived in [42,43] that includes fluctuating boundary structure. Again, we find the appropriate field-dependent redefinition of the parameters to render the charges integrable [12,30,66,[89][90][91].…”

“…Indeed, it is particularly well-adapted to investigate the interplay between radiation and symmetries [17,19,28,[34][35][36][37][38][39]. Furthermore, it allows us to consider simultaneously asymptotically locally flat spacetimes exhibiting null boundaries and asymptotically locally AdS spacetimes with timelike boundaries [26,[40][41][42][43][44][45]. The analyses of these two types of asymptotics are related through a flat limit process [40,46,47].…”

“…To consider asymptotically locally AdS and flat spacetimes in Bondi gauge, one has to allow the boundary structure to fluctuate [19,26,36,[41][42][43]48]. These mild falloffs led to the proposal of an infinite-dimensional enhancement of the BMS group with smooth superrotations in the flat case [19,36,48] and the discovery of BMS-like symmetries in presence of non-vanishing cosmological constant [26,47].…”