The flat limit of three dimensional asymptotically anti-de Sitter spacetimes

TL;DR

This paper explores the connection between three-dimensional asymptotically anti-de Sitter and flat spacetimes by reformulating coordinates and applying a modified Penrose limit, enhancing understanding of holography in flat space.

Contribution

It introduces a novel coordinate reformulation and a modified Penrose limit to relate AdS and flat spacetimes in three dimensions, addressing previous coordinate limitations.

Findings

Established a coordinate transformation linking AdS and flat spacetimes.

Demonstrated a modified Penrose limit connects the two regimes.

Enhanced understanding of holographic properties in flat space.

Abstract

In order to get a better understanding of holographic properties of gravitational theories with a vanishing cosmological constant, we analyze in detail the relation between asymptotically anti-de Sitter and asymptotically flat spacetimes in three dimensions. This relation is somewhat subtle because the limit of vanishing cosmological constant cannot be naively taken in standard Fefferman-Graham coordinates. After reformulating the standard anti-de Sitter results in Robinson-Trautman coordinates, a suitably modified Penrose limit is shown to connect both asymptotic regimes.