Geometric Finiteness, Holography and Quasinormal Modes for the Warped AdS_3 Black Hole

TL;DR

This paper establishes a precise holographic correspondence for Euclidean warped AdS_3 black holes by demonstrating their geometric finiteness and applying Sullivan's theorem to relate bulk hyperbolic structures to boundary conformal structures, leading to holographic quasinormal modes.

Contribution

It introduces a kinematical notion of holography for warped AdS_3 black holes based on geometric finiteness and applies Sullivan's theorem to derive holographic quasinormal modes.

Findings

Euclidean warped AdS_3 black holes are geometrically finite hyperbolic manifolds.

A one-to-one correspondence exists between bulk hyperbolic structure and boundary conformal structure.

Holographic quasinormal modes are obtained for warped AdS_3 black holes.

Abstract

We show that there exists a precise kinematical notion of holography for the Euclidean warped $AdS_3$ black hole. This follows from the fact that the Euclidean warped $AdS_3$ black hole spacetime is a geometrically finite hyperbolic manifold. For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of its boundary. Using this theorem we obtain the holographic quasinormal modes for the warped $AdS_3$ black hole.