Statistics – Computation
Scientific paper
Dec 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phdt........23c&link_type=abstract
Thesis (PHD). THE UNIVERSITY OF TEXAS AT AUSTIN , Source DAI-B 59/06, p. 2801, Dec 1998, 143 pages.
Statistics
Computation
2
Gravitational Radiation, Special Relativity
Scientific paper
The coalescence of two black holes is of tremendous interest for theoretical and astrophysical reasons since binary black hole mergers are expected to be strong sources of gravitational radiation and would be an exciting phenomenon to observe in nature. Researchers are building gravitational wave observatories which will be capable of detecting radiation from such events at the beginning of the next century, opening an entirely new window to observing the universe. This dissertation explores numerical techniques to obtain solutions to the Einstein field equations for black hole spacetimes such as these binary black hole mergers. From these solutions we can characterize the gravitational radiation and the event horizon structure. The emphasis is on developing general algorithms for evolving binary black hole spacetimes with arbitrary momenta and spins so that realistic astrophysical systems can be investigated. To study these highly asymmetrical and singular spacetimes, three dimensional computer models are needed and require supercomputer performance for their execution. The black hole singularities must be excised from the computational domain and a finite outer boundary to the spacetime must be defined. These artificial boundaries of the computational domain prove to be stubborn sources of instabilities in the numerical solutions. Indeed, these instabilities have proven to be the most difficult obstacle to progress within the field. The numerical techniques described in this dissertation were implemented in both simple model problems, prototype three-dimensional black hole evolution codes, and most recently in the sophisticated 3 + 1 Cauchy Code-a collaborative effort to develop a robust, production code for evolving black hole space times under the auspices of the NSF Binary Black Hole Grand Challenge Alliance. The Alliance has made significant progress in developing a suite of numerical algorithms for evolving black hole spacetimes. This dissertation achieved the successful numerical evolution of stationary Kerr black holes, the short term evolution of a boosted Kerr black holes, and the short term evolution of the off-axis approach of binary Kerr black holes. While the results proved a qualified success in evolving binary black holes spacetimes, additional work is recommended to achieve the long-term evolution for the more general problem of co-orbiting binary black holes.
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