Asymptotic Symmetry and the General Black Hole Solution in Ads_3 Gravity

TL;DR

This paper explores the asymptotic symmetry of general black holes in AdS_3 gravity, emphasizing the role of a specific subgroup, and presents a broad class of black hole solutions characterized by infinite conserved quantities.

Contribution

It clarifies the role of the $SL(2; {f R})_{L+R}$ subgroup in asymptotic symmetry and introduces a general black hole solution with infinite conserved quantities.

Findings

Brown-Henneaux asymptotic symmetry described for general black holes

Identification of a key subgroup $SL(2; {f R})_{L+R}$ in symmetry analysis

Construction of a broad class of black hole solutions with infinite conserved quantities

Abstract

We describe the Brown-Henneaux asymptotic symmetry of the general black holes in the Chern-Simons gauge theory of the gauge group $SL(2;{\bf R})_L\times SL(2;{\bf R})_R$. We make it clear that the vector-like subgroup $SL(2; {\bf R})_{L+R}$ plays an essential role in describing the asymptotic symmetry consistently. We find a quite general black hole solution in the $AdS_3$ gravity theory. The solution is specified by an infinite number of conserved quantities which constitute a family of mapping from $S^1$ to the gauge group. The BTZ black hole is one of the simplest case.