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  Spectral approach to axisymmetric evolution of Einstein's equations

Schell, C., & Rinne, O. (2015). Spectral approach to axisymmetric evolution of Einstein's equations. Journal of Physics: Conference Series, 600 (1): 012060. doi:10.1088/1742-6596/600/1/012060.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-27A1-5 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-9957-0
Genre: Journal Article

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 Creators:
Schell, Christian1, Author              
Rinne, Oliver1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 Abstract: We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the occurrence of coordinate singularities on the axis of symmetry and at the origin. Spherical harmonics are manifestly regular on the axis and hence take care of that issue automatically. In addition a spectral approach has computational advantages when the equations are implemented. Therefore we spectrally decompose all the variables in the appropriate harmonics. A central point in the formulation is the gauge choice. One of our results is that the commonly used maximal-isothermal gauge turns out to be incompatible with tensor harmonic expansions, and we introduce a new gauge that is better suited. We also address the regularisation of the coordinate singularity at the origin.

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 Dates: 2014-10-092015
 Publication Status: Published in print
 Pages: 6 pages, based on a talk given by one of the authors at the Spanish Relativity Meeting ERE14 in Valencia
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1410.2548
DOI: 10.1088/1742-6596/600/1/012060
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Title: Journal of Physics: Conference Series
Source Genre: Journal
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Publ. Info: Bristol : IOP Publishing
Pages: - Volume / Issue: 600 (1) Sequence Number: 012060 Start / End Page: - Identifier: ISSN: 1742-6588
CoNE: /journals/resource/111097776606042