Holography for Black Holes in General Relativity and Beyond
Date
2020-08-28
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0000-0001-9444-8110
Type
Thesis
Degree Level
Masters
Abstract
Both extremal and non-extremal Kerr black holes have been considered to be holographically dual to two-dimensional (2D) conformal field theories (CFTs). In this thesis, we study the holography to the case of a rotating Janis-Newman-Winicour (JNW) black holes, a rotating Brans-Dicke-Kerr (BDK) black hole, and an asymptotically anti-de Sitter (AdS) rotating charged black holes in $f$($T$) gravity, where $f(T) = T + \alpha T^2$, where $\alpha$ is a constant. Firstly, we find that the rotating JNW solution does not satisfy the Einstein field equation. Thus, we could not establish a well-defined Kerr/CFT correspondence in this theory. Secondly, we find that the scalar wave equation in the background of BDK black hole is not separable. The existence of the $SL(2,R)_L\times SL(2,R)_R$ symmetry can be found in the radial equation of the scalar probe around the non-extremal black hole. Therefore, the inseparability of the scalar wave equation eliminates the possibility of any holography aspect for BDK black hole. Thirdly, we find that the scalar wave radial equation at the near-horizon region implies the existence of the 2D conformal symmetries. We note that the $2\pi$ identification of the azimuthal angle $\phi$ in the black hole line element, corresponds to a spontaneous breaking of the conformal symmetry by left and right temperatures $T_{L}$ and $T_{R}$, respectively. We show that choosing proper central charges for the dual CFT, we produce exactly the macroscopic Bekenstein-Hawking entropy from the microscopic Cardy entropy for the dual CFT. These observations suggest that the rotating charged AdS black hole in $f$($T$) gravity is dual to a 2D CFT at finite temperatures $T_{L}$ and $T_{R}$ for a specific value of mass $M$, rotational, charge, and $f$($T$) parameters, $\Omega$, $Q$, and $\abs{\alpha}$, respectively.
Description
Keywords
Holography, black holes, conformal field theory, modified gravity.
Citation
Degree
Master of Science (M.Sc.)
Department
Physics and Engineering Physics
Program
Physics