#### Document Type

Dissertation

#### Date of Degree

Summer 2011

#### Degree Name

PhD (Doctor of Philosophy)

#### Degree In

Physics

#### First Advisor

Vincent G. J. Rodgers

#### Abstract

In this thesis we accomplish two goals: We construct a two dimensional conformal field theory (CFT), in the form of a Liouville theory, in the near horizon limit for three and four dimensions black holes. The near horizon CFT assumes the two dimensional black hole solutions that were first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088-104) and later expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two dimensions black holes admit a $Diff(S^1)$ or Witt subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. These charges and lowest Virasoro eigen-modes reproduce the correct Bekenstein-Hawking entropy of the four and three dimensions black holes via the Cardy formula (Bl"ote et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two dimensions CFT's energy momentum tensor is anomalous, i.e. its trace is nonzero. However, In the horizon limit the energy momentum tensor becomes holomorphic equaling the Hawking flux of the four and three dimensions black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamics and statistical quantities for the non local effective action approach.

We also show that the near horizon regime of a Kerr-Newman-$AdS$ ($KNAdS$) black hole, given by its two dimensional analogue a la Robinson and Wilczek, is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The $s$-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence in the appropriate limits. We also compute the Hawking temperature of the $KNAdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.

#### Keywords

Black Holes, Conformal Field Theory, Quantum Gravity, Thermodynamics

#### Pages

x, 88 pages

#### Bibliography

Includes bibliographical references (pages 81-88).

#### Copyright

Copyright 2011 Leo L. Rodriguez