Advertisement

General Relativity and Gravitation

, Volume 40, Issue 5, pp 985–1012 | Cite as

Physical frames along circular orbits in stationary axisymmetric spacetimes

  • Donato Bini
  • Christian Cherubini
  • Andrea Geralico
  • Robert T. Jantzen
Research Article

Abstract

Three natural classes of orthonormal frames, namely Frenet-Serret, Fermi–Walker and parallel transported frames, exist along any timelike world line in spacetime. Their relationships are investigated for timelike circular orbits in stationary axisymmetric spacetimes, and illustrated for black hole spacetimes.

Keywords

Relativistic circular orbits Parallel transport Fermi-Walker transport Black holes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramowicz M.A., Carter B. and Lasota J.P. (1988). Gen. Relat. Grav. 20: 1173 CrossRefADSMathSciNetMATHGoogle Scholar
  2. 2.
    Abramowicz M.A. and Lasota J.P. (1997). Class. Quantum Grav. 14: A23 CrossRefADSMathSciNetMATHGoogle Scholar
  3. 3.
    Jantzen R.T., Carini P. and Bini D. (1992). Ann. Phys. (N.Y.) 215: 1 CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    de Felice F. (1994). Class. Quantum Grav. 11: 1283 CrossRefADSGoogle Scholar
  5. 5.
    Semerák O. (1996). Gen. Relat. Grav. 28: 1151 CrossRefADSMATHGoogle Scholar
  6. 6.
    Bini D., Carini P. and Jantzen R.T. (1997). Int. J. Mod. Phys. D 6: 1 CrossRefADSMathSciNetMATHGoogle Scholar
  7. 7.
    Bini D., Carini P. and Jantzen R.T. (1997). Int. J. Mod. Phys. D 6: 143 CrossRefADSMathSciNetMATHGoogle Scholar
  8. 8.
    Page D. (1998). Class. Quantum Grav. 15: 1669 CrossRefADSMathSciNetMATHGoogle Scholar
  9. 9.
    Bini, D., Carini, P., Jantzen, R.T.: In: Piran, T. (ed.) Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity. World Scientific, Singapore (1998); arXiv e-print: gr-qc/9710051Google Scholar
  10. 10.
    Misner C.W., Thorne K.S. and Wheeler J.A. (1973). Gravitation. Freeman, San Francisco Google Scholar
  11. 11.
    Rindler W. and Perlick V. (1990). Gen. Relat. Grav. 22: 1067 CrossRefADSMathSciNetMATHGoogle Scholar
  12. 12.
    Tartaglia A. (2000). Gen. Relat. Grav. 32: 1745 CrossRefADSMathSciNetMATHGoogle Scholar
  13. 13.
    Bini D. and Jantzen R.T. (2002). General Relativity, Cosmology and Gravitational Lensing. Bibliopolis, Naples Google Scholar
  14. 14.
    Bini D., Jantzen R.T. and Mashhoon B. (2001). Class. Quant. Grav. 18: 653 CrossRefADSMathSciNetMATHGoogle Scholar
  15. 15.
    Rothman T., Ellis G.F.R. and Murugan J. (2001). Class. Quantum Grav. 18: 1217 CrossRefADSMathSciNetMATHGoogle Scholar
  16. 16.
    Maartens R., Mashhoon B. and Matravers D.R. (2002). Class. Quantum Grav. 19: 195 CrossRefADSMathSciNetMATHGoogle Scholar
  17. 17.
    Bini D., Jantzen R.T. and Mashhoon B. (2002). Class. Quantum Grav. 19: 17 CrossRefADSMathSciNetMATHGoogle Scholar
  18. 18.
    Bini D., Cherubini C. and Jantzen R.T. (2002). Class. Quantum Grav. 19: 5481 CrossRefADSMathSciNetMATHGoogle Scholar
  19. 19.
    Bini D., Cherubini C., Cruciani G. and Jantzen R.T. (2004). Int. J. Mod. Phys. D 13: 1771 CrossRefADSMathSciNetMATHGoogle Scholar
  20. 20.
    Bini D. and Jantzen R.T. (2003). Nuovo Cim. B 117: 983 ADSGoogle Scholar
  21. 21.
    Bini D. and Jantzen R.T. (2000). Class. Quantum Grav. 17: 1 MathSciNetGoogle Scholar
  22. 22.
    Iyer B.R. and Vishveshwara C.V. (1993). Phys. Rev. D 48: 5721 CrossRefADSGoogle Scholar
  23. 23.
    Bini D., Merloni A. and Jantzen R.T. (1999). Class. Quantum Grav. 16: 1333 CrossRefADSMathSciNetMATHGoogle Scholar
  24. 24.
    Marck J.A. (1983). Phys. Lett. A 97: 140 CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    Marck J.A. (1986). J. Math. Phys. 27: 1589 CrossRefADSMathSciNetMATHGoogle Scholar
  26. 26.
    Cai Y.Q. and Papini G. (1991). Phys. Rev. Lett. 66: 1259 CrossRefADSGoogle Scholar
  27. 27.
    Bini, D., Jantzen, R.T.: In: Rizzi, G., Ruggiero M.L. (eds.) Relativity in Rotating Frames: Relativistic Physics in Rotating Reference Frames, the series Fundamental Theories of Physics, vol. 135, p. 221. Kluwer, Dordrecht (2004)Google Scholar
  28. 28.
    Bahder T.B.: arXiv e-print: gr-qc/9811009Google Scholar
  29. 29.
    Stephani H., Kramer D., MacCallum M.A.H., Hoenselaers C. and Herlt E. (2003). Exact Solutions of Einstein’s Field Equations, 2nd edn. Cambridge University Press, Cambridge MATHGoogle Scholar
  30. 30.
    Bini D., de Felice F. and Jantzen R.T. (1999). Class. Quantum Grav. 16: 2105 CrossRefADSMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Donato Bini
    • 1
    • 2
    • 3
  • Christian Cherubini
    • 2
    • 4
  • Andrea Geralico
    • 5
  • Robert T. Jantzen
    • 2
    • 6
  1. 1.Istituto per le Applicazioni del Calcolo “M. Picone”, CNRRomeItaly
  2. 2.ICRAUniversity of Rome “La Sapienza”RomeItaly
  3. 3.INFN–Sezione di FirenzePolo ScientificoSesto Fiorentino (FI)Italy
  4. 4.Facoltá di IngegneriaUniversità Campus BiomedicoRomeItaly
  5. 5.Physics Department and ICRAUniversity of Rome “La Sapienza”RomeItaly
  6. 6.Department of Mathematical SciencesVillanova UniversityVillanovaUSA

Personalised recommendations