General Relativity and Gravitation

, Volume 40, Issue 10, pp 2185–2199 | Cite as

Falling into a Schwarzschild black hole

Geometric aspects
Research Article


Consider a radially freely falling observer who plunges into a Schwarzschild black hole. In contrast to a static observer, he will have a different view of the black hole and of the outer sky. Furthermore, the relationship between the proper time of the falling observer and the proper time of a distant static observer differs from the relationship between the proper times of two static observers or two freely falling observers.


Schwarzschild black hole Local observer Proper time Apparent size of a black hole 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramowitz M. and Stegun I.A. (1964). Handbook of Mathematical Functions. Dover Publication, New York MATHGoogle Scholar
  2. 2.
    Ames W.L. and Thorne K.S. (1968). The optical appearance of a star that is collapsing through its gravitational radius. Astrophys. J. 151: 659 CrossRefADSGoogle Scholar
  3. 3.
    Bakala, P., Čermák, P., Hledík, S., Stuchlík, Z., Truparová, K.: Extreme gravitational lensing in the vicinity of Schwarzschild-de Sitter black holes. (arXiv: astro-ph/0709.4274)Google Scholar
  4. 4.
    Carter, B.: Half century of black-hole theory: from physicists “purgatory to mathematicians” paradise. (arXiv: gr-qc/0604064)Google Scholar
  5. 5.
    Crawford P. and Tereno I. (2002). Generalized observers and velocity measurements in general relativity. Gen. Rel. Grav. 34: 2075 MATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Cunningham C.T. (1975). Optical appearances of distant objects to observers near and inside a Schwarzschild black hole. Phys. Rev. D 12: 323–328 CrossRefADSGoogle Scholar
  7. 7.
    Eddington A.S. (1924). A comparison of Whitehead’s and Einstein’s formulas. Nature 113: 192 CrossRefADSGoogle Scholar
  8. 8.
    Faulkner J., Hoyle F. and Narlikar J.V. (1964). On the behavior of radiation near massive bodies. Astrophys. J. 140: 1100 MATHCrossRefADSGoogle Scholar
  9. 9.
    Finkelstein D. (1958). Past–future asymmetry of the gravitational field of a point particle. Phys. Rev. 110: 965–967 MATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Grave, F.: Visualisierungen zum Gravitationskollaps und Wellenfronten in der Allgemeinen Relativitätstheorie (in german). Master thesis, Eberhard–Karls Universität Tübingen (2004)Google Scholar
  11. 11.
    Jaffe J. (1969). Collapsing objects and the background emission of light. Ann. Phys. 55: 374 CrossRefADSGoogle Scholar
  12. 12.
    Janis A.I. (1973). Note on motion in the Schwarzschild field. Phys. Rev. D 8: 2360–2362 CrossRefADSGoogle Scholar
  13. 13.
    Janis A.I. (1977). Motion in the Schwarzschild field: a reply. Phys. Rev. D 15: 3068–3069 CrossRefADSGoogle Scholar
  14. 14.
    Kruskal M.D. (1960). Maximal extension of Schwarzschild metric. Phys. Rev. 119: 1743 MATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Martel K. and Poisson E. (2001). Regular coordinate systems for Schwarzschild and other spherical spacetimes. Am. J. Phys. 69: 476 CrossRefADSGoogle Scholar
  16. 16.
    Misner C.W., Thorne K.S. and Wheeler J.A. (1973). Gravitation. W.H. Freeman, San Francisco Google Scholar
  17. 17.
    Müller, T.: Visualisierung in der Relativitätstheorie (in german). Ph.D. thesis, Eberhard–Karls Universität Tübingen (2006)Google Scholar
  18. 18.
    Novikov, I.D.: Ph.D. thesis. Shternberg Astronomical Institute, Moscow (1963)Google Scholar
  19. 19.
    Oppenheimer J.R. and Snyder H. (1939). On continued gravitational contraction. Phys. Rev. 56: 455 MATHCrossRefADSGoogle Scholar
  20. 20.
    Rindler W. (2001). Relativity—Special, General and Cosmology. Oxford University Press, Oxford Google Scholar
  21. 21.
    Schee J., Stuchlík Z. and Jurán J. (2005). Light escape cones and raytracing in Kerr geometry. Proc. RAGtime 6(7): 143 Google Scholar
  22. 22.
    Semerák O. (1996). What forces act in relativistic gyroscope precession?. Class. Quant. Grav. 13: 2987 MATHCrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Visualisierungsinstitut der Universität StuttgartStuttgartGermany

Personalised recommendations