Advertisement

Astrophysics and Space Science

, Volume 344, Issue 2, pp 437–446 | Cite as

Photons motion in charged Anti-de Sitter black holes

  • J. R. Villanueva
  • Joel Saavedra
  • Marco Olivares
  • Norman Cruz
Original Article

Abstract

In this work we study the null geodesics in the background of Reissner-Nordström Anti de Sitter black hole. We compute the exact trajectories in terms of Weierstrass elliptic functions, obtaining a detailed description of the orbits in terms of the charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.

Keywords

Black holes Elliptic functions 

Notes

Acknowledgements

We are grateful to Prof. Gary Gibbons for his enlightening comments. J.S. was supported by COMISION NACIONAL DE CIENCIAS Y TECNOLOGIA through FONDECYT Grant 1110076, 1090613 and 1110230. Also J.S. work was partially supported by PUCV DI-123.713/2011. N.C. acknowledges the support to this research by CONICYT through Grant No. 1110840. M.O. and J.V. acknowledge the hospitality of the Physics Department of Universidad de Santiago de Chile. M.O. was supported by PUCV through Proyecto DI Postdoctorado 2011. J.V. was supported by Universidad de Tarapacá Grant 4720-11.

References

  1. Chandrasekhar, S.: The Mathematical Theory of Black Holes. Oxford University Press, New York (1983) zbMATHGoogle Scholar
  2. Cherubini, C., Geralico, A., Rueda, J., Ruffini, R.: Phys. Rev. D 79, 124002 (2009) ADSCrossRefGoogle Scholar
  3. Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753–1936 (2006). hep-th/0603057 MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. Cruz, N., Olivares, M., Villanueva, J.R.: Class. Quantum Gravity 22, 1167–1190 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. Damour, T., Ruffini, R.: Phys. Rev. Lett. 35, 463 (1975) ADSCrossRefGoogle Scholar
  6. Einstein, A.: Preuss. Akad. Wiss. Berlin Sitzber., 142 (1917) Google Scholar
  7. Gibbons, G.W., Warnick, C.M., Werner, M.C.: Class. Quantum Gravity 25, 245009 (2008) MathSciNetADSCrossRefGoogle Scholar
  8. Gibbons, G.W., Vyska, M.: Class. Quantum Gravity 29, 065016 (2012) MathSciNetADSCrossRefGoogle Scholar
  9. Hackmann, E., Lammerzahl, C.: Phys. Rev. Lett. 100, 171101 (2008a) MathSciNetADSCrossRefGoogle Scholar
  10. Hackmann, E., Lammerzahl, C.: Phys. Rev. D 78, 024035 (2008b) MathSciNetADSCrossRefGoogle Scholar
  11. Hackmann, E., Kagramanova, V., Kunz, J., Lammerzahl, C.: Phys. Rev. D 78, 124018 (2008). Ibid., (Erratum), 79, 029901 (2009) MathSciNetADSCrossRefGoogle Scholar
  12. Islam, J.N.: The cosmological constant and classical tests of general relativity. Phys. Lett. 97A(6), 239 (1983) MathSciNetADSGoogle Scholar
  13. Kottler, F.: Ann. Phys. 56, 410 (1918) Google Scholar
  14. Jaklitsch, M.J., Hellaby, C., Matravers, D.R.: Gen. Relativ. Gravit. 21, 941 (1989) MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. Kraniotis, G.V., Whitehouse, S.B.: Class. Quantum Gravity 20, 4817–4835 (2003) MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. Kraniotis, G.V.: Class. Quantum Gravity 21, 4743–4769 (2004) MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. Neslusan, L.: Astron. Astrophys. 372, 913 (2001) ADSCrossRefGoogle Scholar
  18. Olivares, M., Saavedra, J., Leiva, C., Villanueva, J.R.: Mod. Phys. Lett. A 26, 2923 (2011). arXiv:1101.0748 [gr-qc] MathSciNetADSCrossRefGoogle Scholar
  19. Peebles, P.J.E.: (1998). astro-ph/9806201
  20. Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559–606 (2003) MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. Punsly, B.: Black Hole Gravitohydromagnetics. Springer, Berlin (2001) zbMATHCrossRefGoogle Scholar
  22. Pugliese, D., Quevedo, H., Ruffini, R.: arXiv:1003.2687 [gr-qc] (2010)
  23. Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. D 84, 044030 (2011a) ADSCrossRefGoogle Scholar
  24. Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. D 83, 104052 (2011b) ADSCrossRefGoogle Scholar
  25. Riess, A.G., et al. (Supernova Search Team Collaboration): Astrophys. J. 607, 665–687 (2004) ADSCrossRefGoogle Scholar
  26. Ruffini, R., Vereshchagin, G., Xue, S.-S.: Phys. Rep. 487(1–4), 1–4 (2010) ADSCrossRefGoogle Scholar
  27. Shutz, B.: A First Course in General Relativity. Cambridge University Press, Cambridge (1990) Google Scholar
  28. Shvartsman, V.F.: Sov. Phys. JETP 33, 475 (1970) ADSGoogle Scholar
  29. Stuchlík, Z., Calvani, M.: Gen. Relativ. Gravit. 23, 507 (1991) ADSCrossRefGoogle Scholar
  30. Stuchlík, Z., Hledík, S.: Phys. Rev. D 60, 044006 (1999) MathSciNetADSCrossRefGoogle Scholar
  31. Stuchlík, Z., Hledík, S.: Acta Phys. Slovaca 52, 363 (2002) Google Scholar
  32. Stuchlík, Z., Slany, P.: Phys. Rev. D 69, 064001 (2004) MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • J. R. Villanueva
    • 1
  • Joel Saavedra
    • 2
  • Marco Olivares
    • 2
  • Norman Cruz
    • 3
  1. 1.Departamento de Física, Facultad de CienciasUniversidad de TarapacáAricaChile
  2. 2.Instituto de FísicaPontificia Universidad de Católica de ValparaísoValparaísoChile
  3. 3.Departamento de Física, Facultad de CienciaUniversidad de Santiago de ChileSantiago 2Chile

Personalised recommendations