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Solutions to Einstein's vacuum equations in three dimensions are locallymaximally symmetric. They are distinguished by their global properties andtheir investigation often requires a choice of gauge. Although analyses of thissort have been performed abundantly, several relevant questions remain. Thesequestions include the interplay between the standard Bondi gauge and theEddington--Finkelstein type of gauge used in the fluid/gravity holographicreconstruction 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 setup a thorough dictionary for the available descriptions with emphasis on therelativistic or Carrollian holographic fluids, which portray the bulk from theboundary in anti-de Sitter or flat instances. A complete presentation ofresidual diffeomorphisms with a preliminary study of their algebra accompaniesthe situations addressed here.

Gauges in Three-Dimensional Gravity and Holographic Fluids