Skip to main content
Log in

The equatorial motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

In this work, we perform a detailed analysis of the equatorial motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime. By working out the orbit equation in the radial direction, we examine possible orbit types. We investigate the conditions for existence of bound orbits in causality-preserving region as well as the conditions for existence of circular orbits for charged and uncharged particles. We also study the effect of NUT parameter on Newtonian orbits. Finally, we give exact analytical solutions of equations of equatorial motion for a charged test particle.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Newman, E., Tamburino, L., Unti, T.: Empty space generalization of the Schwarzschild metric. J. Math. Phys. 4, 915 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Demiański, M., Newman, E.T.: A combined Kerr–NUT solution of the Einstein field equations. Bull. Acad. Polon. Sci. Math. Astron. Phys. 14, 653 (1966)

    MATH  Google Scholar 

  3. Misner, C.W.: The flatter regions of Newman, Unti and Tamburino’s generalized Schwarzschild space. J. Math. Phys. 4, 924 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  4. Bonnor, W.B.: A new interpretation of the NUT metric in general relativity. Math. Proc. Camb. Philos. Soc. 66, 145 (1969)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Miller, J.G.: Global analysis of the Kerr–Taub–NUT metric. J. Math. Phys. 14, 486 (1973)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Nouri-Zonoz, M., Lynden-Bell, D.: Gravitomagnetic lensing by NUT space. Mon. Not. Astron. Soc. 292, 714 (1997)

    Article  ADS  Google Scholar 

  7. Lynden-Bell, D., Nouri-Zonoz, M.: Classical monopoles: Newton, NUT space, gravitomagnetic lensing and atomic spectra. Rev. Mod. Phys. 70, 427 (1998)

    Article  ADS  MATH  Google Scholar 

  8. Bini, D., Cherubini, C., Jantzen, R.T.: On the interaction of massless fields with a gravitomagnetic monopole. Class. Quant. Grav. 19, 5265 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bini, D., Cherubini, C., Jantzen, R.T., Mashhoon, B.: Gravitomagnetism in the Kerr–Newman–Taub–NUT spacetime. Class. Quant. Grav. 20, 457 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Aliev, A.N.: Rotating spacetimes with asymptotic non-flat structure and the gyromagnetic ratio. Phys. Rev. D 77, 044038 (2008)

    Article  ADS  Google Scholar 

  11. Esmer, G.D.: Separability and hidden symmetries of Kerr–Taub–NUT spacetime in Kaluza–Klein theory. Grav. Cosmol. 19, 139 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Liu, C., Chen, S., Ding, C., Jing, J.: Particle acceleration on the background of the Kerr–Taub–NUT Spacetime. Phys. Lett. B 701, 285 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  13. Zimmerman, R.L., Shahir, B.Y.: Geodesics for the NUT metric and gravitational monopoles. Gen. Relativ. Gravit. 21(8), 821 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Kagramanova, V., Kunz, J., Hackmann, E., Lämmerzahl, C.: Analytic treatment of complete and incomplete geodesics in Taub–NUT space–times. Phys. Rev. D 81, 124044 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  15. Abdujabbarov, A.A., Ahmedov, B.J., Kagramanova, V.G.: Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge. Gen. Relativ. Gravit. 40, 2515 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Abdujabbarov, A.A., Ahmedov, B.J., Shaymatov, S.R., Rakhmatov, A.S.: Penrose process in Kerr–Taub–NUT spacetime. Astrophys. Space Sci. 334, 237 (2011)

    Article  ADS  MATH  Google Scholar 

  17. Grenzebach, A., Perlick, V., Lämmerzahl, C.: Photon regions and shadows of Kerr–Newman–NUT black holes with a cosmological constant. Phys. Rev. D 89, 124004 (2014)

    Article  ADS  Google Scholar 

  18. Pradhan, P.: Circular geodesics in the Kerr–Newman–Taub–NUT spacetime. Class. Quant. Grav. 32, 165001 (2015)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Jefremov, P.I., Perlick, V.: Circular motion in NUT space–time. Class. Quant. Grav. 33, 245014 (2016)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Clément, G., Guenouche, M.: Motion of charged particles in a NUTty Einstein–Maxwell spacetime and causality violation. Gen. Relativ. Gravit 50, 60 (2018)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Mukharjee, S., Chakraborty, S., Dadhich, N.: On some novel features of the Kerr–Newman–NUT spacetime. Eur. Phys. J. C 79, 161 (2019)

    Article  ADS  Google Scholar 

  22. Abbott, B.P., et al.: LIGO Scientific and Virgo Collaborations, Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  23. Grunau, S., Kagramanova, V.: Geodesics of electrically and magnetically charged test particles in the Reissner–Nordström spacetime: analytical solutions. Phys. Rev. D 83, 044009 (2011)

    Article  ADS  Google Scholar 

  24. Flathmann, K., Grunau, S.: Analytic solutions of the geodesic equation for Einstein–Maxwell–dilaton–axion black holes. Phys. Rev. D 92, 104027 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  25. Pugliese, D., Quevedo, H., Ruffini, R.: Motion of charged test particles in Reissner–Nordström spacetime. Phys. Rev. D 83, 104052 (2011)

    Article  ADS  Google Scholar 

  26. Olivares, M., Saavedra, J., Leiva, C., Villanueva, J.: Motion of charged particles on the Reissner–Nordström (Anti)–de Sitter black holes. Mod. Phys. Lett. A 26, 2923 (2011)

    Article  ADS  MATH  Google Scholar 

  27. Hackmann, E., Xu, H.: Charged particle motion in Kerr–Newmann space–times. Phys. Rev. D 87, 124030 (2013)

    Article  ADS  Google Scholar 

  28. Soroushfar, S., Saffari, R., Kazempour, S., Grunau, S., Kunz, J.: Detailed study of geodesics in the Kerr–Newman–(A)dS spacetime and the rotating charged black hole spacetime in \(f(R)\) gravity. Phys. Rev. D 94, 024052 (2016)

    Article  MathSciNet  Google Scholar 

  29. Cebeci, H., Özdemir, N., Şentorun, S.: Motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime and analytical solutions. Phys. Rev. D 93, 104031 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  30. Bardeen, J.M., Press, W.H., Teukolsky, S.A.: Rotating black holes: locally nonrotating frames, energy extraction and scalar synchrotron radiation. Astrophys. J. 178, 347 (1972)

    Article  ADS  Google Scholar 

  31. Dadhich, N., Kale, P.P.: Equatorial circular geodesics in the Kerr–Newman geometry. J. Math. Phys. 18, 1727 (1977)

    Article  ADS  Google Scholar 

  32. Pugliese, D., Quevedo, H., Ruffini, R.: Equatorial circular orbits of neutral test particles in the Kerr–Newman spacetime. Phys. Rev. D 88, 024042 (2013)

    Article  ADS  Google Scholar 

  33. Stuchlík, Z., Slaný, P.: Equatorial circular orbits in the Kerr–de Sitter spacetimes. Phys. Rev. D 69, 064001 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  34. Slaný, P., Pokorná, M., Stuchlík, Z.: Equatorial circular orbits in Kerr–anti-de Sitter spacetimes. Gen. Relativ. Gravit 45, 2611 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Wald, R.M.: General Relativity. The University of Chicago Press, Chicago (1984)

    Book  MATH  Google Scholar 

  36. Chandrasekhar, S.: The Mathematical Theory of Black Holes. Clarendon Press, London (1983)

    MATH  Google Scholar 

  37. Carter, B.: Hamilton–Jacobi and Schrodinger separable solutions of Einstein’s equations. Commun. Math. Phys. 10, 280 (1968)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. Carter, B.: Global structure of the Kerr family of gravitational fields. Phys. Rev. 174, 1559 (1968)

    Article  ADS  MATH  Google Scholar 

  39. Debever, R., Kamran, N., Mc Lenaghan, R.G.: Exhaustive integration and a single expression for the general solution of the type D vacuum and electrovac field equations with cosmological constant for a nonsingular aligned Maxwell field. J. Math. Phys. 25, 1955 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  40. Frolov, V.P., Krtous, P., Kubizňák, D.: Separability of Hamilton–Jacobi and Klein–Gordon equations in general Kerr–NUT–AdS spacetimes. J. High Energy Phys. 02, 005 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  41. Zakharov, A.F.: On the hotspot near a Kerr black hole: Monte Carlo simulations. Mon. Not. R. Astron. Soc. 269, 283 (1994)

    Article  ADS  Google Scholar 

  42. Mino, Y.: Perturbative approach to an orbital evolution around a supermassive black hole. Phys. Rev. D 67, 084027 (2003)

    Article  ADS  Google Scholar 

  43. Pugliese, D., Quevedo, H.: The ergoregion in the Kerr spacetime: properties of the equatorial circular motion. Eur. Phys. J. C 75, 234 (2015)

    Article  ADS  Google Scholar 

  44. Pugliese, D., Quevedo, H.: Observers in Kerr spacetimes. Eur. Phys. J. C 78, 69 (2018)

    Article  ADS  Google Scholar 

  45. O’Neill, B.: The Geometry of Kerr Black Holes. A K Peters/CRC Press, Wellesley (1995)

    MATH  Google Scholar 

  46. Wilkins, D.C.: Bound geodesics in the Kerr metric. Phys. Rev. D 5, 814 (1972)

    Article  ADS  Google Scholar 

  47. Dereli, T., Tucker, R.W.: On the detection of scalar field induced space–time torsion. Mod. Phys. Lett. A 17, 421 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. Cebeci, H., Dereli, T., Tucker, R.W.: Autoparallel orbits in Kerr Brans–Dicke spacetimes. Int. J. Mod. Phys. D 13, 137 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. Wang, Z.X., Guo, D.R.: Special Functions. World Scientific Publishing Co., Singapore (1989)

    Book  Google Scholar 

  50. Drasco, S., Hughes, S.A.: Rotating black hole orbit functionals in the frequency domain. Phys. Rev. D 69, 044015 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  51. Fujita, R., Hikida, W.: Analytical solutions of bound timelike geodesic orbits in Kerr spacetime. Class. Quant. Grav. 26, 135002 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. Hackmann, E., Lämmerzahl, C.: Observables for bound orbital motion in axially symmetric space–times. Phys. Rev. D 85, 044049 (2012)

    Article  ADS  Google Scholar 

  53. Chakraborty, C., Bhattacharyya, S.: Does the gravitomagnetic monopole exist? A clue from a black hole X-ray binary. Phys. Rev. D 98, 043021 (2018)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank anonymous reviewers for their suggestions and comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hakan Cebeci.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cebeci, H., Özdemir, N. & Şentorun, S. The equatorial motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime. Gen Relativ Gravit 51, 85 (2019). https://doi.org/10.1007/s10714-019-2569-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-019-2569-3

Keywords

Navigation