Advertisement

General Relativity and Gravitation

, Volume 44, Issue 2, pp 509–533 | Cite as

Detailed study of null and timelike geodesics in the Alcubierre warp spacetime

  • Thomas MüllerEmail author
  • Daniel Weiskopf
Research Article

Abstract

The geodesic equation of the Alcubierre warp spacetime is converted into its non-affinely parametrized form for a detailed discussion of the motion of particles and the visual effects as observed by a traveller inside the warp bubble or a person looking from outside. To include gravitational lensing for point-like light sources, we present a practical approach using the Jacobi equation and the Sachs bases. Additionally, we consider the dragging and geodesic precession of particles due to the warp bubble.

Keywords

Alcubierre warp spacetime Non-affinely parametrized geodesics Relativistic visualization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Morris M.S., Thorne K.S.: Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity. Am. J. Phys. 56, 395–412 (1988)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Alcubierre M.: The warp drive: hyper-fast travel within general relativity. Class. Quantum Grav. 11, L73–L77 (1994)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Clark C., Hiscock W.A., Larson S.L.: Null geodesics in the Alcubierre warp-drive spacetime: the view from the bridge. Class. Quantum Grav. 16, 3965–3972 (1999)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Weiskopf, D.: Four-dimensional non-linear ray tracing as a visualization tool for gravitational physics.In: Proceedings of the IEEE Conference on Visualization, IEEE Computer Society Press, 2000, pp. 445–448Google Scholar
  5. 5.
    Hiscock W.A.: Quantum effects in the Alcubierre warp-drive spacetime. Class. Quantum Grav. 14, L183–L188 (1997)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Pfenning M.J., Ford L.H.: The unphysical nature of ‘warp drive’. Class. Quantum Grav. 14, 1743–1751 (1997)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    van den Broeck C.: A ‘warp drive’ with more reasonable total energy requirements. Class. Quantum Grav. 16, 3973–3979 (1999)ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Lobo F.S.N., Visser M.: Fundamental limitations on ‘warp drive’ spacetimes. Class. Quantum Grav. 21, 5871–5892 (2004)MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Müller T., Grave F.: GeodesicViewer—a tool for exploring geodesics in the theory of relativity. Comput. Phys. Commun. 181, 413–419 (2010)ADSzbMATHCrossRefGoogle Scholar
  10. 10.
    Wald R.M.: General relativity. The University of Chicago Press, Chicago (1984)zbMATHGoogle Scholar
  11. 11.
    Schneider P., Ehlers J., Falco E.E.: Gravitational Lenses. Springer, Berlin (1992)CrossRefGoogle Scholar
  12. 12.
    The Milky Way panorama is by ESO/S. Brunier, http://www.eso.org/public/images/eso0932a
  13. 13.
    Weiskopf D., Kraus U., Ruder H.: Searchlight and doppler effects in the visualization of special relativity: a corrected derivation of the transformation of radiance. ACM Trans. Graph. 18, 278–292 (1999)CrossRefGoogle Scholar
  14. 14.
    Nwankwo, A., Thompson, J., Ishak, M.: Luminosity distance and redshift in the Szekeres inhomogeneous cosmological models. arXiv:1005.2989v1 [astro-ph]Google Scholar
  15. 15.
    Rindler W.: Relativity—Special, General and Cosmology. Oxford University Press, Oxford (2001)Google Scholar
  16. 16.
    GNU Scientific Library (GSL), http://www.gnu.org/software/gsl
  17. 17.
    Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P.: Numerical Recipes in C. Cambridge University Press, Cambridge (2002)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Visualisierungsinstitut der Universität Stuttgart (VISUS)StuttgartGermany

Personalised recommendations