Gauges in Three-Dimensional Gravity and Holographic Fluids

TL;DR

This paper explores the relationships between different gauges in three-dimensional gravity solutions and their implications for holographic fluids, aiming to unify descriptions in various boundary conditions.

Contribution

It establishes a comprehensive dictionary linking gauge choices in 3D gravity to holographic fluid descriptions, including residual diffeomorphisms and their algebra.

Findings

Clarified the interplay between Bondi, Eddington--Finkelstein, and Fefferman--Graham gauges.

Developed a detailed mapping for relativistic and Carrollian holographic fluids.

Analyzed residual diffeomorphisms and their algebraic structures.

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.