Skip to main content
Log in

Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

We have developed a realistic, fully general relativistic computer code to simulate optical projection in a strong, spherically symmetric gravitational field. The standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitterspacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from the static radius. Simulations include effects of the gravitational lensing, multiple images, Doppler and gravitational frequency shift, as well as the intensity amplification. The code generates images of the sky for the static observer and a movie simulations of the changing sky for the radially free-falling observer. Techniques of parallel programming are applied to get a high performance and a fast run of the BHC simulation code.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Einstein: “Lens-like action of a star by the deviation of light in the gravitational field”, Science, Vol. 84, (1936), pp. 506–507.

    Article  ADS  Google Scholar 

  2. C.T. Cunningham: “Optical Appearance of Distant Observers near and inside a Schwarzschild Black Hole”, Phys. Rev. D, Vol. 12, (1975), pp. 323–328.

    Article  ADS  Google Scholar 

  3. W. Benger: “Simulation of a Black Hole by Raytracing”, In: Relativity and Scientific Computing: Computer Algebra, Numerics, Visualization, Springer-Verlag Telos, 1996.

  4. A. J. S. Hamilton: “Black Hole Flight Simulator”, Bulletin of the American Astronomical Society, Vol. 36, (2004), pp. 810.

    ADS  Google Scholar 

  5. D. Kobras, D. Weiskopf and H. Ruder: “Image-based rendering and general relativity”, In: WSCG 2001 Conference Proceedings, University of West Bohemia, Pilsen, 2001, pp. 130–137.

    Google Scholar 

  6. R.J. Nemiroff: “Visual distortion near a neutron star a and black hole”, Am. J. Phys., Vol. 61, (1993), pp. 619–631.

    Article  ADS  Google Scholar 

  7. H.P. Nollert, H. Ruder, H. Herold and U. Kraus: “The relativistic looks of a neutron star”, Astron. Astrophys., Vol. 208, (1989), pp. 153–156.

    ADS  Google Scholar 

  8. H.C. Ohanian: “The black hole as a gravitational lens”, Am. J. Phys., Vol. 55, (1987), pp. 428–432.

    Article  ADS  Google Scholar 

  9. S.U. Viergutz: “Image generation in Kerr geometry. I. Analytical investigations on the stationary emitter-observer problem”, Astron. Astrophys., Vol. 272, (1993), pp. 355–377.

    ADS  MathSciNet  Google Scholar 

  10. L.M. Krauss and M.S. Turner: “The Cosmological constant is back”, Gen. Relat. Gravit., Vol. 27, (1995), pp. 1137–1144.

    Article  MATH  ADS  Google Scholar 

  11. J.P. Ostriker and P.J. Steinhardt: “The Observational case for a low density universe with a nonzero cosmological constant”, Nature, Vol. 377, (1995), pp. 600–602.

    Article  ADS  Google Scholar 

  12. Z. Stuchlík and S. Hledík: “Some properties of the Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes”, Phys. Rev. D, Vol. 60, (1999), art. 044006.

    Google Scholar 

  13. Z. Stuchlík and K. Plšková: “Optical apperance of isotropically radiating sphere in the Schwarzschild-de Sitter spacetime”, In: Proceedings of RAGtime 4/5, eds. S. Hledík and Z. Stuchlík, Silesian University in Opava, Opava, 2004, pp. 167–185.

    Google Scholar 

  14. P. Bakala, P. Čermák, S. Hledík, Z. Stuchlík and K. Truparová Plšková: “A virtual trip to the Schwarzschild-de Sitter black hole”, In: Proceedings of RAGtime 6/7, eds. S. Hledík and Z. Stuchlík, Silesian University in Opava, Opava, 2005, pp. 11–28.

    Google Scholar 

  15. Relativistic and particle physics and its astrophysical aplications, “Czech research project MSM 4781305903”, http://www.physics.cz/research/.

  16. Z. Stuchlík, P. Slaný and S. Hledík: “Equilibrium configurations of perfect fluid orbiting Schwarzschild-de Sitter black holes”, Astron. Astrophys., Vol. 363, (2000), pp. 425–439.

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pavel Bakala.

About this article

Cite this article

Bakala, P., Čermák, P., Hledík, S. et al. Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes. centr.eur.j.phys. 5, 599–610 (2007). https://doi.org/10.2478/s11534-007-0033-6

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11534-007-0033-6

Keywords

PACS (2006)

Navigation