Abstract

Despite the success of General Relativity in the past century, a quantum description of gravity remains one of the most active areas of research in theoretical physics today. While gravity becomes dominant at large scales where classical physics is an appropriate effective theory, the study of very massive systems on a very small scale would require a quantum theory of gravity. A quantum description of gravity is also needed to have a grand unified theory of all the fundamental forces. The most prominent candidate for a theory of quantum gravity is currently String Theory. The discovery of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence shows a duality between gravity solutions from String Theory in anti-de Sitter (AdS) spacetimes and conformal field theories (CFT) that reside on its boundary. Particularly, in a certain limit, the correspondence means that the study of certain classes of Quantum Field Theory in flat spacetime can be mapped to classical black hole solutions in five-dimensional anti-de Sitter spacetimes, the latter being considered an approximation to solutions from String Theory. A strong interest in the study of five-dimensional black hole solutions in anti-de Sitter spacetimes then follows naturally from the AdS/CFT correspondence. One of the predictions of the AdS/CFT correspondence is a relation between the conformal anomaly of the CFT and the trace of the energy momentum theory of the garivational theory. Another interesting prediction is an equivalence between the AdS background energy of black hole solutions and the vacuum energy of the dual CFT on the boundary. The study of black hole thermodynamics in anti-de Sitter spacetimes presents certain challenges that do not exist in flat spacetimes. Particularly, certain isometric charges as well as the action become divergent on the boundary. Our goal here is to study the thermodynamics of the most general solution of blackholes in five-dimensional AdS spacetimes. In doing so, we will address the aforementioned difficulties and discuss the appropriate solutions for them. We will also calculate the conformal anomaly and vacuum energy of the dual CFT then calculate the corresponding quantities in the black hole solution. This will provide a test for the AdS/CFT correspondence in the most general case of black hole solutions in five dimensions AdS spacetimes.

Department

Physics Department

Degree Name

MS in Physics

Graduation Date

Fall 7-26-2020

Submission Date

July 2020

First Advisor

Awad, Adel

Second Advisor

NA

Third Advisor

NA

Committee Member 1

AlFiky, Mohammad

Committee Member 2

Lashin, ElSayed

Committee Member 3

Hamed, Ahmed

Extent

152 p.

Document Type

Master's Thesis

Library of Congress Subject Heading 1

Physics

Rights

The author retains all rights with regard to copyright. The author certifies that written permission from the owner(s) of third-party copyrighted matter included in the thesis, dissertation, paper, or record of study has been obtained. The author further certifies that IRB approval has been obtained for this thesis, or that IRB approval is not necessary for this thesis. Insofar as this thesis, dissertation, paper, or record of study is an educational record as defined in the Family Educational Rights and Privacy Act (FERPA) (20 USC 1232g), the author has granted consent to disclosure of it to anyone who requests a copy. The author has granted the American University in Cairo or its agents a non-exclusive license to archive this thesis, dissertation, paper, or record of study, and to make it accessible, in whole or in part, in all forms of media, now or hereafter known.

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