16
views
0
recommends
+1 Recommend
0 collections
0
shares
• Record: found
• Abstract: found
• Article: found
Is Open Access

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

Preprint

, , ,

Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### 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.

### Most cited references7

• Record: found

### Three-Dimensional Massive Gauge Theories

(1982)
Bookmark
• Record: found
• Abstract: found
• Article: found
Is Open Access

### Geometry of the 2+1 Black Hole

(1993)
The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti-de Sitter space by a discrete subgroup of $$SO(2,2)$$. The generic black hole is a smooth manifold in the metric sense. The surface $$r=0$$ is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at $$r=0$$ to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti-de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum . A thorough classification of the elements of the Lie algebra of $$SO(2,2)$$ is given in an Appendix.
Bookmark
• Record: found
• Abstract: found
• Article: found
Is Open Access

### Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes

(2001)
We obtain exact expressions for the quasi-normal modes of various spin for the BTZ black hole. These modes determine the relaxation time of black hole perturbations. Exact agreement is found between the quasi-normal frequencies and the location of the poles of the retarded correlation function of the corresponding perturbations in the dual conformal field theory. This then provides a new quantitative test of the AdS/CFT correspondence.
Bookmark

### Author and article information

###### Journal
17 December 2009
2010-06-05
###### Article
10.1088/0264-9381/27/16/165012
0912.3584