Geometrical Finiteness, Holography, and the BTZ Black Hole

TL;DR

This paper demonstrates how Sullivan's theorem mathematically formalizes a 3D holographic principle, linking the hyperbolic structure of certain 3D manifolds to boundary Teichmuller space, with implications for the Euclidean BTZ black hole.

Contribution

It applies Sullivan's theorem to establish a precise mathematical foundation for the 3D holographic principle in the context of the Euclidean BTZ black hole.

Findings

Hyperbolic structure determined by boundary Teichmuller space

Mathematical formalization of 3D holography

Insights into Euclidean BTZ black hole geometry

Abstract

We show how a theorem of Sullivan provides a precise mathematical statement of a 3d holographic principle, that is, the hyperbolic structure of a certain class of 3d manifolds is completely determined in terms of the corresponding Teichmuller space of the boundary. We explore the consequences of this theorem in the context of the Euclidean BTZ black hole in three dimensions.