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Large Black Holes in the Randall-Sundrum II Model Open Access


Other title
Black Hole
Randall-Sundrum Model
Type of item
Degree grantor
University of Alberta
Author or creator
Yaghoobpour Tari, Shima
Supervisor and department
Don N. Page
Examining committee member and department
Toby Wiseman (Physics, Imperial College London)
Dmitri Pogosyan (Physics)
Valeri P. Frolov (Physics)
Vincent Bouchard (Mathematical and Statistical Sciences)
Sharon Morsink (Physics)
Department of Physics

Date accepted
Graduation date
Doctor of Philosophy
Degree level
The Einstein equation with a negative cosmological constant \lambda in the five dimensions for the Randall-Sundrum II model, which includes a black hole, has been solved numerically. We have constructed an AdS_5-CFT_4 solution numerically, using a spectral method to minimize the integral of the square of the error of the Einstein equation, with 210 parameters to be determined by optimization. This metric is conformal to the Schwarzschild metric at an AdS5 boundary with an infinite scale factor. So, we consider this solution as an infinite-mass black hole solution. We have rewritten the infinite-mass black hole in the Fefferman-Graham form and obtained the numerical components of the CFT energy-momentum tensor. Using them, we have perturbed the metric to relocate the brane from infinity and obtained a large static black hole solution for the Randall-Sundrum II model. The changes of mass, entropy, temperature and area of the large black hole from the Schwarzschild metric are studied up to the first order for the perturbation parameter 1/(−\lambda M^2). The Hawking temperature and entropy for our large black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(−\lambda_5). Figueras, Lucietti, and Wiseman found an AdS_5-CFT_4 solution using an independent and different method from us, called the Ricci-DeTurck-flow method. Then, Figueras and Wiseman perturbed this solution in a same way as we have done and obtained the solution for the large black hole in the Randall-Sundrum II model. These two numerical solutions are the first mathematical proofs for having a large black hole in the Randall-Sundrum II. We have compared their results with ours for the CFT energy-momentum tensor components and the perturbed metric. We have shown that the results are closely in agreement, which can be considered as evidence that the solution for the large black hole in the Randall-Sundrum II model exists.
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