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Numerical relativity using a generalized harmonic decomposition

Pretorius, Frans (2005) Numerical relativity using a generalized harmonic decomposition. Classical and Quantum Gravity, 22 (2). pp. 425-451. ISSN 0264-9381. doi:10.1088/0264-9381/22/2/014.

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A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates are treated as independent functions, and encode the coordinate freedom of solutions. Techniques are discussed to impose particular gauge conditions through a specification of the source functions. A 3D, free evolution, finite difference code implementing this system of equations with a scalar field matter source is described. The second-order-in-space-and-time partial differential equations are discretized directly without the use of first-order auxiliary terms, limiting the number of independent functions to 15—ten metric quantities, four source functions and the scalar field. This also limits the number of constraint equations, which can only be enforced to within truncation error in a numerical free evolution, to four. The coordinate system is compactified to spatial infinity in order to impose physically motivated, constraint-preserving outer boundary conditions. A variant of the cartoon method for efficiently simulating axisymmetric spacetimes with a Cartesian code is described that does not use interpolation, and is easier to incorporate into existing adaptive mesh refinement packages. Preliminary test simulations of vacuum black-hole evolution and black-hole formation via scalar field collapse are described, suggesting that this method may be useful for studying many spacetimes of interest.

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Additional Information:© 2005 IOP Publishing Ltd. Received 30 July 2004, in final form 6 December 2004, Published 3 January 2005, Print publication: Issue 2 (21 January 2005). I would like to thank Matthew Choptuik for many stimulating discussions about the work presented here. I gratefully acknowledge research support from NSF PHY-0099568, NSF PHY-0244906 and Caltech’s Richard Chase Tolman Fund. Simulations were performed on UBC’s vn cluster, (supported by CFI and BCKDF), and the Westgrid cluster (supported by CFI, ASRI and BCKDF).
Issue or Number:2
Record Number:CaltechAUTHORS:PREcqg05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:519
Deposited By: Archive Administrator
Deposited On:12 Jul 2005
Last Modified:12 Jul 2022 19:43

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