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Global Differential Geometry and Global Analysis 1984 pp 316–339Cite as

Conformal orbits of electromagnetic Riemannian curvature tensors electromagnetic implies gravitational radiation

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1156))

Abstract

Electromagnetic curvature structures (c.s.) are defined as being bilinear in the two electromagnetic field matrices and electrovac c.s. by having the el.magn. energy-momentum as Einstein tensor. There is a one-parameter familiy of electrovac c.s. having never a component in the space of constant curvatures. Their non-Weyl component is uniquely determined by the el.magn. energy-momentum, and in general they have a Weyl component. It is shown that el.magn. implies gravitational radiation, and coversely that el.magn. gravitational radiation is induced by el.magn. radiation. A structure theory of c.s. is described with morphisms as linear conformal transformations (i.e. Lorentztransformations and dilatations) such that the above properties of c.s., and many others, are orbit properties.

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Authors and Affiliations

  1. Mathematisches Institut, Technische Universität Berlin, Limastr. 1, 1000, Berlin 37

    Hans Tilgner

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  1. Hans Tilgner
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Dirk Ferus Robert B. Gardner Sigurdur Helgason Udo Simon

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© 1985 Springer-Verlag

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Tilgner, H. (1985). Conformal orbits of electromagnetic Riemannian curvature tensors electromagnetic implies gravitational radiation. In: Ferus, D., Gardner, R.B., Helgason, S., Simon, U. (eds) Global Differential Geometry and Global Analysis 1984. Lecture Notes in Mathematics, vol 1156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075101

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  • DOI: https://doi.org/10.1007/BFb0075101

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15994-0

  • Online ISBN: 978-3-540-39698-7

  • eBook Packages: Springer Book Archive

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