Title page for ETD etd-03202007-163153

Type of Document Dissertation
Author Dorband, Ernst Nils
Author's Email Address dorband@cct.lsu.edu
URN etd-03202007-163153
Title Computing and Analyzing Gravitational Radiation in Black Hole Simulations Using a New Multi-Block Approach to Numerical Relativity
Degree Doctor of Philosophy (Ph.D.)
Department Physics & Astronomy
Advisory Committee
Advisor Name Title
Manuel Tiglio Committee Chair
Edward Seidel Committee Member
James Matthews Committee Member
Juhan Frank Committee Member
Burak Aksoylu Dean's Representative
  • sources of gravitational waves
  • kerr black holes
  • high order numerical methods
  • multi-patch
Date of Defense 2007-02-15
Availability unrestricted
Numerical simulations of Kerr black holes are presented and the excitation of quasinormal modes is studied in detail. Issues concerning the extraction of gravitational waves from numerical space-times and analyzing them in a systematic way are discussed.

A new multi-block infrastructure for solving first order symmetric hyperbolic time dependent partial differential equations is developed and implemented in a way that stability is guaranteed for arbitrary high order accurate numerical schemes. Multi-block methods make use of several coordinate patches to cover a computational domain. This provides efficient, flexible and very accurate numerical schemes.

Using this code, three dimensional simulations of perturbed Kerr black holes are carried out. While the quasinormal frequencies for such sources are well known, until now little attention has been payed to the relative excitation strength of different modes. If an actual perturbed Kerr black hole emits two distinct quasinormal modes that are strong enough to be detected by gravitational wave observatories, these two modes can be used to test the Kerr nature of the source. This would provide a strong test of the so called no hair theorem of general relativity. A systematic method for analyzing ringdown waveforms is proposed. The so called time shift problem, an ambiguity in the definition of excitation amplitudes, is identified and it is shown that this problem can be avoided by looking at appropriately chosen relative mode amplitudes. Rotational mode coupling, the relative excitation strength of co- and counter rotating modes and overtones for slowly and rapidly spinning Kerr black holes are studied.

A method for extracting waves from numerical space-times which generalizes one of the standard methods based on the Regge-Wheeler-Zerilli perturbation formalism is presented. Applying this to evolutions of single perturbed Schwarzschild black holes, the accuracy of the new method is compared to the standard approach and it is found that the errors resulting from the former are one to several orders of magnitude below the ones from the latter. It is demonstrated that even at large extraction radii (r=80M), the standard extraction approach produces errors that are dominantly of systematic nature and not due to numerical inaccuracies.

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