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Some aspects of motion in the Kerr field

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Czechoslovak Journal of Physics Aims and scope

Abstract

We find that the Kerr field, the simplest relativistic gravitational field of a rotating source, may help in (pre-)collimation of cosmic jets emanating from many active galactic nuclei. Solving the geodesic motion in the Kerr field, we use in part a tetrad approach — the description of quantities by their physically measured components in the locally Cartesian frame of a local observer (rather than by their coordinate components). The stationary frames, the most important local frames in the Kerr spacetime, are reviewed and their properties discussed. We use the Newtonian “force” language to interpret the occurrence of the “rotospheres”, the toroidal regions that circle round the Kerr sources; in these regions, the 4-acceleration of a stationary observer depends on his orbital angular velocity in a way going against common intuition. We give the rotospheres in various Kerr spacetimes and introduce a new class of privileged observers (“extremally accelerated observers”). We then generalize this approach to any motion in any spacetime. In the Kerr spaces, we construct the cones generated by directions along which photons can escape to infinity from a given point. The results are consistent with the expected influence of rotational dragging for black holes, whereas they are rather complicated for naked singularities.

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References

  1. Schwarzschild K.:in Sitzber. Deut. Akad. Wiss. Berlin, Kl. Math.-Phys. Tech., 3 Februar, 1916, p. 189.

  2. Oppenheimer J. R. and Snyder H.: Phys. Rev.56 (1939) 455.

    Google Scholar 

  3. Zel'dovich Ya. B. and Novikov I. D.: Relyativistskaya astrofizika. Nauka, Moscow, 1967 (English translation: Relativistic Astrophysics. University of Chicago Press, Chicago, 1971).

    Google Scholar 

  4. Hoyle F. and Lyttleton R. A.: Proc. Cambr. Phil. Soc.35 (1939) 405.

    Google Scholar 

  5. von Weizsäcker C. F.: Z. Astrophys.22 (1944) 319.

    Google Scholar 

  6. von Weizsäcker C. F.: Z. Naturforsch.3a (1948) 524.

    Google Scholar 

  7. Wheeler J. A.: American Scientist56 (1968) 1.

    Google Scholar 

  8. Giacconi R., Gursky H., Paolini F. R., and Rossi B. B.: Phys. Rev. Lett.9 (1962) 439.

    Google Scholar 

  9. Schmidt M.: Nature197 (1963) 1040.

    Google Scholar 

  10. Hewish A., Bell S. J., Pilkington J. D. H., Scott P. F., and Collins R. A.: Nature217 (1968) 709.

    Google Scholar 

  11. Seyfert C. K.: Astrophys. J.97 (1943) 28.

    Google Scholar 

  12. Jennison R. C. and Das Gupta M. K.: Nature172 (1953) 96.

    Google Scholar 

  13. Curtis H. D.: Publ. Lick Obs.13 (1918), No. 9, 31.

    Google Scholar 

  14. Zel'dovich Ya. B.: Dokl. Akad. Nauk SSSR155 (1964) 67 [English translation: Sov. Phys. Dokl.9 (1964) 195].

    Google Scholar 

  15. Salpeter E. E.: Astrophys. J.140 (1964) 796.

    Google Scholar 

  16. Lynden-Bell D.: Nature223 (1969) 690.

    Google Scholar 

  17. Bardeen J. M.: Nature226 (1970) 64.

    Google Scholar 

  18. Kerr R. P.: Phys. Rev. Lett.11 (1963) 237.

    Google Scholar 

  19. Boyer R. H. and Lindquist R. W.: J. Math. Phys.8 (1967) 265.

    Google Scholar 

  20. Rees M. J.: Sci. Am.263 (1990), No. 5, 26.

    Google Scholar 

  21. Blandford R. D.:in 300 Years of Gravitation (edited by S. W. Hawking and W. Israel). Cambridge University Press, Cambridge 1987, p. 277.

    Google Scholar 

  22. Lynden-Bell D. and Gilmore G. (editors): Baryonic Dark Matter. Kluwer, Dordrecht, 1990.

    Google Scholar 

  23. Clayton D. D., Newman M. J., and Talbot R. J., Jr.: Astrophys. J.201 (1975) 489.

    Google Scholar 

  24. Bahcall J. N. and Ostriker J. P.: Nature256 (1975) 23.

    Google Scholar 

  25. Hawking S. W.: Nature248 (1974) 30.

    Google Scholar 

  26. Refsdal S.: Mon. Not. R. Astron. Soc.,128 (1964) 295.

    Google Scholar 

  27. Paczyński B.: Nature321 (1986) 419.

    Google Scholar 

  28. Smarr L. L. (editor): Sources of Gravitational Radiation (Proc. of the Battelle Seattle Workshop). Cambridge University Press, Cambridge, 1979.

    Google Scholar 

  29. Carter B.:in Gravitation in Astrophysics, Cargèse 1986 (NATO ASI series. Series B, Physics; Vol. 156, edited by B. Carter and J. B. Hartle). Plenum Press, New York, 1987, p. 63.

    Google Scholar 

  30. Eisenstaedt J.: Gen. Rel. Grav.23 (1991) 75.

    Google Scholar 

  31. Michell J.: Philos. Trans. R. Soc. London74 (1784) 35.

    Google Scholar 

  32. Priestley J.: The History and Present State of Discoveries Relating to Vision, Light and Colours. J. Johnson, London, 1772, p. 786.

    Google Scholar 

  33. Novikov I. D. and Thorne K. S.:in Black Holes (edited by C. DeWitt and B. S. DeWitt). Gordon and Breach, New York, 1973, p. 343.

    Google Scholar 

  34. Blandford R. D. and Thorne K. S.:in General Relativity, An Einstein Centenary Survey (edited by S. W. Hawking and W. Israel). Cambridge University Press, Cambridge, 1979, p. 454.

    Google Scholar 

  35. Begelman M. C., Blandford R. D., and Rees M. J.: Rev. Mod. Phys.56 (1984) 225.

    Google Scholar 

  36. Blandford R. D.:in Active Galactic Nuclei (edited by T. J.-L. Courvoisier and M. Mayor). Springer-Verlag, Berlin Heidelberg, 1990, p. 161.

    Google Scholar 

  37. Wiita P. J.:in Beams and Jets in Astrophysics (edited by P. A. Hughes). Cambridge University Press, Cambridge, 1991, p. 379.

    Google Scholar 

  38. Misner C. W., Thorne K. S., and Wheeler J. A.: Gravitation. Freeman, San Francisco, 1973.

    Google Scholar 

  39. Chandrasekhar S.: The Mathematical Theory of Black Holes. Oxford University Press, Oxford, 1983.

    Google Scholar 

  40. Novikov I. D. and Frolov V. P.: Fizika tchernykh dyr. Nauka, Moscow, 1986 (English translation: Physics of Black Holes. Kluwer, Dordrecht, 1989).

    Google Scholar 

  41. Lynden-Bell D.: Phys. Scripta17 (1978) 185.

    Google Scholar 

  42. Abramowicz M. A. and Piran T.: Astrophys. J.241 (1980) L7.

    Google Scholar 

  43. Sikora M.: Mon. Not. R. Astron. Soc.196 (1981) 257.

    Google Scholar 

  44. Lovelace R. V. E.: Nature262 (1976) 649.

    Google Scholar 

  45. Blandford R. D.: Mon. Not. R. Astron. Soc.176 (1976) 465.

    Google Scholar 

  46. Blandford R. D. and Znajek R. L.: Mon. Not. R. Astron. Soc.179 (1977) 433.

    Google Scholar 

  47. Rees M. J.: Nature229 (1971) 312 and 510.

    Google Scholar 

  48. Padman R., Lasenby A. N., and Green D. A.:in Beams and Jets in Astrophysics (edited by P. A. Hughes). Cambridge University Press, Cambridge, 1991, p. 484.

    Google Scholar 

  49. Blandford R. D.:in Superluminal Radio Sources (edited by J. A. Zensus and T. J. Pearson). Cambridge University Press, Cambridge, 1987, p. 310.

    Google Scholar 

  50. Carter B.: Phys. Rev.174 (1968) 1559.

    Google Scholar 

  51. Bičák J., Semerák O., and Hadrava P.: Mon. Not. R. Astron. Soc.263 (1993) 545.

    Google Scholar 

  52. Semerák O.:in Trends in Physics (Abstracts of the 8th Gen. Conf. of the EPS, edited by F. Pleiter). Print productions b.v., Ursem, 1990, p. 87.

    Google Scholar 

  53. Bičák J., Semerák O., and Hadrava P.: MPA 596, Preprint Max-Planck-Institut für Physik und Astrophysik, Institut für Astrophysik, July 1991.

  54. Bičák J., Semerák O., and Hadrava P.:in MG-6, Proc. of the 6th Marcel Grossmann Meeting on Gen. Rel. (edited by H. Sato and T. Nakamura). World Sci., Singapore, 1992, p. 674.

    Google Scholar 

  55. Bičák J.:in GR-12, Abstracts of the 12th Int. Conf. on Gen. Rel. and Grav. (edited by N. Ashby and P. L. Bender). Univ. of Colorado, Boulder, 1989, Vol. 2, p. 403.

    Google Scholar 

  56. de Felice F.: Astron. Astrophys.45 (1975) 65.

    Google Scholar 

  57. Israel W.: Phys. Rev. D2 (1970) 641.

    Google Scholar 

  58. Stewart J. and Walker M.: Springer Tracts Mod. Phys.69 (1973) 69.

    Google Scholar 

  59. Sharp N. A.: Gen. Rel. Grav.10 (1979) 659.

    Google Scholar 

  60. Dymnikova I. G.: Usp. Fiz. Nauk148 (1986) 393 (English translation: Sov. Phys. Usp.29 (1986) 215).

    Google Scholar 

  61. Bičák J., Stuchlík Z., and Balek V.: Bull. Astron. Inst. Czechosl.40 (1989) 65.

    Google Scholar 

  62. Balek V., Bičák J., and Stuchlík Z.: Bull. Astron. Inst. Czechosl.40 (1989) 133.

    Google Scholar 

  63. Semerák O.: Gen. Rel. Grav.25 (1993) 1041.

    Google Scholar 

  64. Abramowicz M. A. and Lasota J. P.: Acta Phys. Polon. B5 (1974) 327.

    Google Scholar 

  65. de Felice F. and Usseglio-Tomasset S.: Class. Q. Gravity8 (1991) 1871.

    Google Scholar 

  66. Semerák O.: Astron. Astrophys., to appear (1994).

  67. Abramowicz M. A.: Mon. Not. R. Astron. Soc.245 (1990) 733.

    Google Scholar 

  68. de Felice F.: Mon. Not. R. Astron. Soc.252 (1991) 197.

    Google Scholar 

  69. Holzmüller G.: Z. Math. Phys.15 (1870) 69.

    Google Scholar 

  70. Mach E.: Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit. Prag, 1872, pp. 47–50.

  71. Einstein A.: Vierteljahrschrift für gerichtliche Medizin und öffentliches Sanitätswesen44 (1912) 37.

    Google Scholar 

  72. Einstein A.: Phys. Z.14 (1913) 1249.

    Google Scholar 

  73. Mashhoon B., Hehl F. W., and Theiss D. S.: Gen. Rel. Grav.16 (1984) 711.

    Google Scholar 

  74. Jantzen R. T., Carini P., and Bini D.: Annals Phys.215 (1992) 1.

    Google Scholar 

  75. Abramowicz M. A. and Prasanna A. R.: Mon. Not. R. Astron. Soc.245 (1990) 720.

    Google Scholar 

  76. Abramowicz M. A.:in The Renaissance of General Relativity and Cosmology (edited by G. F. R. Ellis, A. Lanza and J. C. Miller). Cambridge University Press, Cambridge, 1993, p. 40.

    Google Scholar 

  77. Abramowicz M. A., Carter B., and Lasota J. P.: Gen. Rel. Grav.20 (1988) 1173.

    Google Scholar 

  78. Thorne K. S., Price R. H., and Macdonald D. A. (editors): Black Holes: The Membrane Paradigm. Yale University Press, New Haven, 1986.

    Google Scholar 

  79. Semerák O.: submitted to Nuovo Cimento B.

  80. Abramowicz M. A., Nurowski P., and Wex N.: Class. Q. Gravity10 (1993) L183.

    Google Scholar 

  81. Keres H.: Zh. Eksp. Teor. Fiz.52 (1967) 768.

    Google Scholar 

  82. Bardeen J. M.:in Black Holes (edited by C. DeWitt and B. S. DeWitt). Gordon and Breach, New York, 1973, p. 215.

    Google Scholar 

  83. Semerák O.: submitted to Am. J. Phys.

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  1. Department of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00, Praha 8, Czech Republic

    Oldřich Semerák

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Thanks are due to Prof. J. Bičák for reading the manuscript and suggesting several improvements in the text, and to Dr. P. Hadrava for help with the figures. The work was partially supported by the grant GACR-0503 of the Grant Agency of the Czech Republic and by the grant GAUK-318 of the Charles University, Prague.

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Semerák, O. Some aspects of motion in the Kerr field. Czech J Phys 45, 1–22 (1995). https://doi.org/10.1007/BF01690211

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