Quartic equations and classification of Riemann tensors in general relativity |
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| Authors: | J E Aman R A d'Inverno G C Joly M A H MacCallum |
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| Institution: | (1) Institute of Theoretical Physics, University of Stockholm, Vanadisvägen 9, S-113 46 Stockholm, Sweden;(2) Faculty of Mathematical Studies, University of Southampton, SO9 5NH Southampton, UK;(3) Astronomy Unit, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, E1 4NS London, UK;(4) Present address: Department of Computer Science, University College London, Gower St., WC1E 6BT London, UK |
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| Abstract: | For space-times in general relativity, the Petrov classification of the Weyl conformai curvature and the Pleba ski or Segre classification of the Ricci tensor each depend on the properties of the roots of quartic equations. The coefficients in these quartic equations are in general complicated functions of the space-time coordinates. We review the general theory of quartic equations, and discuss algorithms for determining the existence and values of multiple roots. We consider practical implementation of an algorithm and the consequent Petrov classification. Tests of programs embodying this algorithm, using the computer algebra system CLASSI based on SHEEP, are reported. |
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