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Topics in Black Hole Perturbation Theory and the Visualization of Curved Spacetime


Zimmerman, Aaron Benjamin (2013) Topics in Black Hole Perturbation Theory and the Visualization of Curved Spacetime. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8809-P894.


This thesis presents recent research into analytic topics in the classical theory of General Relativity. It is a thesis in two parts. The first part features investigations into the spectrum of perturbed, rotating black holes. These include the study of near horizon perturbations, leading to a new generic frequency mode for black hole ringdown; an treatment of high frequency waves using WKB methods for Kerr black holes; and the discovery of a bifurcation of the quasinormal mode spectrum of rapidly rotating black holes. These results represent new discoveries in the field of black hole perturbation theory, and rely on additional approximations to the linearized field equations around the background black hole. The second part of this thesis presents a recently developed method for the visualization of curved spacetimes, using field lines called the tendex and vortex lines of the spacetime. The works presented here both introduce these visualization techniques, and explore them in simple situations. These include the visualization of asymptotic gravitational radiation; weak gravity situations with and without radiation; stationary black hole spacetimes; and some preliminary study into numerically simulated black hole mergers. The second part of thesis culminates in the investigation of perturbed black holes using these field line methods, which have uncovered new insights into the dynamics of curved spacetime around black holes.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:General Relativity, Black Holes, Black Hole Perturbations, Numerical Relativity, Tensor Visualization
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Chen, Yanbei
Group:Astronomy Department
Thesis Committee:
  • Chen, Yanbei (chair)
  • Adhikari, Rana
  • Carroll, Sean M.
  • Ott, Christian D.
Defense Date:7 May 2013
Non-Caltech Author Email:aaronbzimmerman (AT)
Record Number:CaltechTHESIS:05152013-113945625
Persistent URL:
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Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7713
Deposited By: Aaron Zimmerman
Deposited On:17 May 2013 22:55
Last Modified:04 Mar 2020 22:06

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