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18 - Kundt solutions

Published online by Cambridge University Press:  04 February 2010

Jerry B. Griffiths
Affiliation:
Loughborough University
Jiří Podolský
Affiliation:
Charles University, Prague
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Summary

Solutions are said to belong to Kundt's class if they admit a null geodesic congruence, generated by a vector field k, which is shear-free, twist-free and expansion-free. They include the pp-waves and plane wave space-times that have been described in the previous chapter. The whole class, initially investigated by Kundt (1961, 1962) in the case of vacuum or with an aligned pure radiation field, is however much wider. Because the null vector field k is not in general covariantly constant, the rays of the corresponding non-expanding waves are not necessarily parallel, as in the case of pp-waves, and the wave surfaces need not be planar. This greater freedom permits, for example, the presence of a cosmological constant Λ or aligned electromagnetic fields, both null and non-null.

For vacuum or some specific matter content, generalised Goldberg—Sachs theorems imply that the Kundt space-times must be algebraically special, that is of Petrov type II, D, III or N (or conformally flat), with k being a repeated principal null direction of the Weyl tensor. Any Einstein—Maxwell and pure radiation fields must also be aligned: that is, k is the common eigendirection of the Weyl and Ricci tensor.

A number of physically interesting space-times of this class are explicitly known. These will be briefly described in this chapter, with emphasis given to those that describe exact non-expanding gravitational waves of various kinds.

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Publisher: Cambridge University Press
Print publication year: 2009

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  • Kundt solutions
  • Jerry B. Griffiths, Loughborough University, Jiří Podolský, Charles University, Prague
  • Book: Exact Space-Times in Einstein's General Relativity
  • Online publication: 04 February 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511635397.019
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  • Kundt solutions
  • Jerry B. Griffiths, Loughborough University, Jiří Podolský, Charles University, Prague
  • Book: Exact Space-Times in Einstein's General Relativity
  • Online publication: 04 February 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511635397.019
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Kundt solutions
  • Jerry B. Griffiths, Loughborough University, Jiří Podolský, Charles University, Prague
  • Book: Exact Space-Times in Einstein's General Relativity
  • Online publication: 04 February 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511635397.019
Available formats
×