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Wave Maps in General Relativity

  • Chapter
On Einstein’s Path

Abstract

Wave maps from a pseudo-Riemannian manifold of hyperbolic (Lorentzian) signature (V, g) into a pseudo-Riemannian manifold are the generalization of the usual wave equations for scalar functions on (V, g). They are the counterpart in hyperbolic signature of the harmonic mappings between properly Riemannian manifolds. The first wave maps to be considered in physics were the σ-models, e.g., the mapping from the Minkowski spacetime into the 3-sphere which models the classical dynamics of 4-meson fields linked by the relation

$$ \sum\limits_{a = 1}^4 {|{f_a}} {|^2} = 1.$$

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Authors
  1. Yvonne Choquet-Bruhat
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Editors and Affiliations

  1. Department of Physics, Queens College, Flushing, NY, 11367, USA

    Alex Harvey

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© 1999 Springer Science+Business Media New York

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Choquet-Bruhat, Y. (1999). Wave Maps in General Relativity. In: Harvey, A. (eds) On Einstein’s Path. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1422-9_11

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  • DOI: https://doi.org/10.1007/978-1-4612-1422-9_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7137-6

  • Online ISBN: 978-1-4612-1422-9

  • eBook Packages: Springer Book Archive

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