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.

arXiv comment44 Pages, Latex, V2

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Cited by in corpus (30)

• Carrollian Perspective on Celestial Holography
• Bridging Carrollian and Celestial Holography
• Carroll Expansion of General Relativity
• Magic Fermions: Carroll and Flat Bands
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
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• Holographic Lorentz and Carroll Frames
• Flat from anti-de Sitter
• 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability
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• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
• Ehlers, Carroll, Charges and Dual Charges
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• Carrollian limit of quadratic gravity
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• Boundary Conditions for Warped AdS${}_3$ in Quadratic Ensemble