Enhanced Asymptotic Symmetry Algebra of 2+1 Dimensional Flat Space

TL;DR

This paper introduces new boundary conditions for 2+1 dimensional flat space gravity, expanding the asymptotic symmetry algebra to include a $ ext{BMS}_3$ algebra and affine $ ext{U}(1)$ currents, with applications to Topologically Massive Gravity.

Contribution

It generalizes previous boundary conditions, derives the resulting extended asymptotic symmetry algebra, and explores effects on central charges and entropy in Einstein and Topologically Massive Gravity.

Findings

Extended asymptotic symmetry algebra includes $ ext{BMS}_3$ and affine $ ext{U}(1)$ currents.

Central extensions are modified by the gravitational Chern-Simons term.

Thermal entropy formulas are obtained for solutions under new boundary conditions.

Abstract

In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in 2+1 dimensions with vanishing cosmological constant that are a generalization of the Barnich-Comp{\`e}re boundary conditions gr-qc/0610130. These new boundary conditions lead to an asymptotic symmetry algebra that is generated by a $\mathfrak{bms}_3$ algebra and two affine $\hat{\mathfrak{u}}(1)$ current algebras. We then apply these boundary conditions to Topologically Massive Gravity (TMG) and determine how the presence of the gravitational Chern-Simons term affects the central extensions of the asymptotic symmetry algebra. We furthermore determine the thermal entropy of solutions obeying our new boundary conditions for both Einstein gravity and TMG.