Exact Results for the BTZ Black Hole

TL;DR

This paper reviews exact mathematical results related to the BTZ black hole, including its structure, formation, entropy, and decay, providing a rigorous understanding of its properties and microscopic description.

Contribution

It presents new exact analytic results on the formation, entropy, and decay of the BTZ black hole using rigorous mathematical theorems and conformal field theory insights.

Findings

Exact determination of the Choptuik scaling parameter.

Proof of a No Hair Theorem from hyperbolic geometry.

Microscopic understanding of entropy and decay rates.

Abstract

In this review, we summarize exact results for the three-dimensional BTZ black hole. We use rigorous mathematical results to clarify the general structure and properties of this black hole spacetime and its microscopic description. In particular, we study the formation of the black hole by point particle collisions, leading to an exact analytic determination of the Choptuik scaling parameter. We also show that a `No Hair Theorem' follows immediately from a mathematical theorem of hyperbolic geometry, due to Sullivan. A microscopic understanding of the Bekenstein-Hawking entropy, and decay rate for massless scalars, is shown to follow from standard results of conformal field theory.