Skip to main content
SpringerLink
Log in

Gödel black hole, closed timelike horizon and the study of particle emissions

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

Abstract

We show that a particle, with positive orbital angular momentum, following an outgoing null/timelike geodesic, shall never reach the closed timelike horizon present in the (4 + 1)-dimensional rotating Gödel black hole space–time. Therefore a large part of this space–time remains inaccessible to a large class of geodesic observers, depending on the conserved quantities associated with them. We discuss how this fact and the existence of the closed timelike curves present in the asymptotic region make the quantum field theoretic study of the Hawking radiation, where the asymptotic observer states are a pre-requisite, unclear. However, the semi classical approach provides an alternative to verify the Smarr formula derived recently for the rotating Gödel black hole. We present a systematic analysis of particle emissions, specifically for scalars, charged Dirac spinors and vectors, from this black hole via the semiclassical complex path method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gödel K.: Rev. Mod. Phys. 21, 447 (1949)

    Article  MATH  ADS  Google Scholar 

  2. Reboucas M.J., Tiomno J.: Phys. Rev. D 28, 1251 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  3. Reboucas M.J. et al.: Phys. Rev. D 32, 3309 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  4. Gauntlett J.P. et al.: Class. Quant. Grav. 20, 4587 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. Herdeiro C.A.R.: Nucl. Phys. B 665, 189 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Gimon E., Hashimoto A.: Phys. Rev. Lett. 91, 021601 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  7. Gibbons, G.W., et al.: arXiv: hep-th/0504080

  8. Herdeiro C.A.R.: Class. Quant. Grav. 20, 4891 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Konoplya R.A., Abdalla E.: Phys. Rev. D 71, 084015 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  10. Boyda E.K. et al.: Phys. Rev. D 67, 106003 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  11. Herdeiro C.A.R. et al.: Phys. Rev. D 69, 066010 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  12. Mann R.B. et al.: JHEP 0504, 49 (2005)

    Google Scholar 

  13. Mann R.B. et al.: Phys. Lett. B 620, 1 (2005)

    Article  ADS  Google Scholar 

  14. Wu S.Q.: Phys. Rev. Lett. 100, 121301 (2008)

    Article  ADS  Google Scholar 

  15. Kerner R., Mann R.B.: Phys. Rev. D 75, 084022 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  16. Chen S. et al.: Phys. Rev. D 78, 064030 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  17. Li W. et al.: Class. Quant. Grav. 26, 055008 (2009)

    Article  ADS  Google Scholar 

  18. Barnich G., Compere G.: Phys. Rev. Lett. 95, 031302 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  19. Hawking S.W.: Commun. Math. Phys. 43, 199 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  20. Traschen, J.: An introduction to Black hole evaporation. In: Bytsenko, A., Williams, F. (eds.) Mathematical Methods of Physics, Proceedings of the 1999 Londrina Winter School. World Scientific (2000). arXiv:gr-qc/0010055

  21. Kraus, P., Wilczek, F.: arxiv:gr-qc/9406042, Nucl. Phys. B 437, 231 (1995)

    Google Scholar 

  22. Kraus P., Keski-Vakkuri E.: Nucl. Phys. B 491, 249 (1997)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. Parikh M.K., Wilczek F.: Phys. Rev. Lett. 85, 5042 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  24. Parikh M.K.: Int. J. Mod. Phys. D 13, 2351 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  25. Srinivasan K., Padmanabhan T.: Phys. Rev. D 60, 24007 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  26. Padmanabhan T. et al.: Mod. Phys. Lett. A 16, 571 (2001)

    Article  MathSciNet  Google Scholar 

  27. Padmanabhan T. et al.: Class. Quant. Grav. 19, 2671 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  28. Medved A.J.M.: Phys. Rev. D 66, 12409 (2002)

    Google Scholar 

  29. Jiang Q. et al.: Phys. Rev. D 73, 064003 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  30. Zhang J., Zhao Z.: Phys. Lett. B 638, 110 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  31. Zhao L.: Commun. Theor. Phys. 47, 835 (2007)

    Article  Google Scholar 

  32. Kerner R., Mann R.B.: Phys. Rev. D 73, 104010 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  33. Wilczek F. et al.: Phys. Rev. D 74, 044017 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  34. Kerner R., Mann R.B.: Class. Quant. Grav. 25, 095014 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  35. Kerner R., Mann R.B.: Phys. Lett. B 665, 277 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  36. Di Criscienzo R., Vanzo L.: Europhys. Lett. 82, 60001 (2008)

    Article  Google Scholar 

  37. Li R., Ren J.R.: Phys. Lett. B 661, 370 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  38. Li R., Ren J.R.: Class. Quant. Grav. 25, 125016 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  39. Jiang Q.Q.: Phys. Lett. B 666, 517 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  40. Jiang Q.Q.: Phys. Rev. D 78, 044009 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  41. Banerjee R., Majhi B.R.: JHEP 0806, 095 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  42. Majhi B.R.: Phys. Rev. D 79, 044005 (2009)

    Article  ADS  Google Scholar 

  43. Majhi, B.R., Samanta, S.: arXiv:hep-th/0901.2258

  44. Angheben M. et al.: JHEP 05, 014 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  45. Medved A., Vagenas E.: Mod. Phys. Lett. A 20, 2449 (2005)

    Article  MATH  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, India

    Sourav Bhattacharya

  2. Department of Physics and Astrophysics, West Bengal State University, Barasat, North 24 Paraganas, West Bengal, India

    Anirban Saha

Authors
  1. Sourav Bhattacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anirban Saha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anirban Saha.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhattacharya, S., Saha, A. Gödel black hole, closed timelike horizon and the study of particle emissions. Gen Relativ Gravit 42, 1809–1823 (2010). https://doi.org/10.1007/s10714-010-0948-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-010-0948-x

Keywords

Search

Navigation