Miens of The Three Dimensional Black Hole

TL;DR

This paper analyzes the properties and interpretations of the rotating three-dimensional Einstein-Anti-de-Sitter black hole, highlighting its topological features, relation to string theory, and significance in broader gravitational contexts.

Contribution

It demonstrates that this black hole is the most general solution in its class and explores its topological and string-theoretic interpretations.

Findings

Black hole is the most general Einstein-Anti-de-Sitter solution.

Interpretation of the integral of motion as spin.

Connection to string theory via WZWN sigma model.

Abstract

Some aspects of the rotating three-dimensional Einstein-Anti-de-Sitter black hole solution, constructed recently by Banados, Teitelboim and Zanelli are discussed. It is shown explicitly that this black hole represents the most general black hole type solution of the Einstein-Anti-de-Sitter theory. The interpretation of one of the integrals of motion as the spin is discussed. Its physics relies on the topological structure of the black hole manifold, and the notion of simultaneity of space-like separated intervals. The relationship of the black hole solution to string theory on a $2 + 1$ dimensional target space is examined, and it is shown that the black hole can be understood as a part of the full axion-dilaton-gravity, realized as a WZWN $\sigma $ model. In conclusion, the pertinence of this solution to four-dimensional black strings and topologically massive gravity is pointed out.