Gauges in Three-Dimensional Gravity and Holographic Fluids

TL;DR

This work builds a detailed dictionary connecting Bondi, fluid/gravity derivative-expansion, and Fefferman–Graham gauges for three-dimensional gravity, covering both locally AdS (bulk with negative cosmological constant) and flat (Carrollian/ Carrollian-fluid) limits. It identifies the full solution spaces in each gauge, characterizes the residual diffeomorphisms, and shows how Bondi data map to a specific hydrodynamic frame while Fefferman–Graham data organize at leading/subleading orders. A key result is the explicit relation between Bondi frame data and the broader fluid/gravity data, enabling translation of bulk diffeomorphisms into boundary hydrodynamic frame changes and vice versa. This lays the groundwork for computing asymptotic charges and their algebras in 3D, with potential extensions to higher dimensions and deeper insights into holographic dualities for AdS and flat spacetimes.

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.