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Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves

Rinne, Oliver (2008) Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves. Classical and Quantum Gravity, 25 (13). Art. No. 135009. ISSN 0264-9381. doi:10.1088/0264-9381/25/13/135009.

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This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such schemes that have been proposed in the literature and show that some of their elliptic equations are indefinite, thus potentially admitting nonunique solutions and causing numerical solvers based on classical relaxation methods to fail. A new scheme is then presented that does not suffer from these problems. We use our numerical implementation to study the gravitational collapse of Brill waves. A highly prolate wave is shown to form a black hole rather than a naked singularity.

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Additional Information:Copyright © Institute of Physics and IOP Publishing Limited 2008. Received 26 February 2008, in final form 17 April 2008. Published 17 June 2008. Print publication: Issue 13 (7 July 2008). The author wishes to thank Sergio Dain, David Garfinkle, John Stewart and Darragh Walsh for helpful discussions on this work. He gratefully acknowledges funding through a Research Fellowship at King’s College Cambridge. Earlier parts of this work were supported by grants to Caltech from the Sherman Fairchild Foundation, NSF grant PHY-0601459 and NASA grant NNG05GG52G.
Issue or Number:13
Record Number:CaltechAUTHORS:RINcqg08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10957
Deposited By: Archive Administrator
Deposited On:20 Jun 2008
Last Modified:12 Jul 2022 19:47

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