The Properties of Spherical Geodesics in the Kerr Metric

Part of the Astrophysics and Space Science Library book series (ASSL, volume 454)


This small methodological chapter is devoted to considering the motion of particles along spherical geodesical trajectories around rotating black holes. The study of this motion is necessary for understanding the inner structure of the disc tilted to the equatorial plane of the rotating black hole. Moreover, this chapter uses a special approach to find out how the values that are measured in a local Lorentz frame of observers falling freely in an axially symmetric gravitational field are related to each other. This approach allows us to understand better the basic principles of measuring physical values in general relativity. These basic principles, which are systematically presented in the next chapter, are required for a more comprehensive understanding the structure of relativistic tilted accretion discs.


  1. Bardeen JM (1973) Timelike and null geodesics in the Kerr metric. In: Dewitt C, Dewitt BS (eds) Black holes (Les Astres Occlus). Gordon and Breach, New York, pp 215–239Google Scholar
  2. Bardeen JM, Petterson JA (1975) The Lense-Thirring effect and accretion disks around Kerr black holes. Astrophys J 195:L65. ADSCrossRefGoogle Scholar
  3. Bardeen JM, Press WH, Teukolsky SA (1972) Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys J 178:347–370. ADSCrossRefGoogle Scholar
  4. Carter B (1968) Global structure of the Kerr family of gravitational fields. Phys Rev 174:1559–1571. ADSCrossRefGoogle Scholar
  5. Lightman AP, Press WH, Price RH, Teukolsky SA (1975) Problem book in relativity and gravitation. Princeton University Press, PrincetonzbMATHGoogle Scholar
  6. Misner CW, Thorne KS, Wheeler JA (1977) Gravitation, vol 3. Princeton University Press, PrincetonGoogle Scholar
  7. Thorne KS, Price RH, MacDonald DA (1986) Black holes: the membrane paradigm. Yale University Press, New HavenzbMATHGoogle Scholar
  8. Wilkins DC (1972) Bound geodesics in the Kerr metric. Phys Rev D 5:814–822. ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Sternberg Astronomical InstituteLomonosov Moscow State UniversityMoscowRussia
  2. 2.Kazan Federal UniversityKazanRussia

Personalised recommendations