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Republication of: On the transition from wave optics to geometric optics in general relativity

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Abstract

This paper considers the relationship between electromagnetic waves and the geometric optics approximation in general relativity. The approximation is widely used in predictions of observations in astronomy and cosmology, for example in gravitational lensing and the cosmic microwave background. Its properties are thus of considerable significance. The paper’s author was a Golden Oldies board member and a prominent author and editor for Springer. It complements other Golden Oldies by Ehlers showing the importance and influence of his attention to issues concerning the relation of exact physical theories and their approximations.

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Notes

  1. This research has been sponsored by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force.

  2. Translator’s note: The original is “normal hyperbolisch”. This term was used at the time for what is today usually called “Lorentzian”.

  3. Occasionally, it is stated that the Eqs. (1) and (2) were only valid in uniformally moving bodies. This is wrong as the electron theoretical-statistical derivation of these equations shows: A. N. Kaufmann, Ann. Phys. New York 18, 264 [1962].

  4. From now on the permittivity will no longer appear explicitly, and we take \(\varepsilon \) to indicate a “small” parameter. Translator’s note: For better readability we use the symbol \(\varepsilon \) only for the small parameter and denote the permittivity by \(\epsilon \).

  5. The original is “Verzerrung (Scherung)” meaning “distortion (shear)”.

  6. A typo in the second label was corrected.

References

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Author information

Author notes

  1. Jürgen Ehlers (Deceased 20 May 2008).

Authors and Affiliations

  1. The University of Texas, Austin, TX, USA

    Jürgen Ehlers

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  1. Jürgen Ehlers
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Additional information

Editorial responsibility Malcolm A. H. MacCallum, E-mail: m.a.h.maccallum@qmul.ac.uk.

Publisher's Note

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An editorial note to this paper can be found in this issue at https://doi.org/10.1007/s10714-021-02894-0

Original paper: “Zum Übergang von der Wellenoptik zur geometrischen Optik in der allgemeinen Relativitätstheorie”, Z. Naturforschung, 22a, 1328–1333 (1967).

Translated and republished by permission of De Gruyter.

Translated by Jörg Frauendiener Mathematics and Statistics, University of Otago, P. O. Box 56, Dunedin 9054, New Zealand E-mail: joerg.frauendiener@otago.ac.nz.

In the original, almost all footnotes simply gave citations to the literature. We have moved the whole bibliography to the end of the text. The only translated original footnotes are now numbered 2 and 3. The rest of the present footnotes are translator’s notes.

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Ehlers, J. Republication of: On the transition from wave optics to geometric optics in general relativity. Gen Relativ Gravit 54, 40 (2022). https://doi.org/10.1007/s10714-021-02894-0

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  • DOI: https://doi.org/10.1007/s10714-021-02894-0

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