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General Relativity and Gravitation

, Volume 2, Issue 4, pp 303–312 | Cite as

On the gravitational field of a massless particle

  • P. C. Aichelburg
  • R. U. Sexl
Research Articles

Abstract

The gravitational field of a massless point particle is first calculated using the linearized field equations. The result is identical with the exact solution, obtained from the Schwarzschild metric by means of a singular Lorentz transformation. The gravitational field of the particle is nonvanishing only on a plane containing the particle and orthogonal to the direction of motion. On this plane the Riemann tensor has a δ-like singularity and is exactly of Petrov typeN.

Keywords

Exact Solution Field Equation Differential Geometry Gravitational Field Lorentz Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Tolman, R. C. (1934).Relativity, Thermodynamics and Cosmology, Oxford.Google Scholar
  2. 2.
    Peres, A. (1960).Phys. Rev.,118, 1105.Google Scholar
  3. 3.
    Bonnor, W. B. (1969).Comm. Math. Phys.,13, 163.Google Scholar
  4. 4.
    Bonnor, W. B. (1970).Int. Jour. Theor. Phys.,3, No. 1, p. 57.Google Scholar
  5. 5.
    Bonnor, W. B. (1970).Int. Jour. Theor. Phys.,3, No. 4, p. 257.Google Scholar
  6. 6.
    See e.g. Gelfand, I. and Schilov, G. (1967).Verallgemeinerte Funktionen, Bd. I, VEB Berlin.Google Scholar
  7. 7.
    Hegarty, J. C. (1969).Nuovo Cim.,61B, 47.Google Scholar
  8. 8.
    See e.g. Adler, Bazin and Schiffer (1965).Introduction to General Relativity, p.176, McGraw-Hill.Google Scholar
  9. 9.
    Jordan, P., Kundt, W. and Ehlers, J. (1960).Akad. Wiss. Lit. Mainz Abh. Math. Nat. Kl.,7, 21.Google Scholar
  10. 10.
    Ehlers, J. and Kundt, W. (1962). Article in:Gravitation, An Introduction to Current Research, ed. L. Wirten, p. 85, New York, John Wiley.Google Scholar
  11. 11.
    Pirani, F. A. E. (1959).Proc. Roy. Soc. A,252, 96.Google Scholar
  12. 12.
    Penrose, R. (1968). inBattelle Rencontres 1967. Eds. C. M. DeWitt and J. A. Wheeler, p. 198, Benjamin.Google Scholar

Copyright information

© Plenum Publishing Company Limited 1971

Authors and Affiliations

  • P. C. Aichelburg
    • 1
  • R. U. Sexl
    • 1
  1. 1.Institut für Theoretische Physik der Universität WienAustria

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