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Axially Symmetric Type N Space-Time with Causality Violating Curves and the von Zeipel Cylinder

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Abstract

An axially symmetric nonvacuum solution of the Einstein field equations, regular everywhere and free from curvature divergence is presented. The matter-energy content is a the pure radiation field satisfying the energy conditions, and the metric is of type N in the Petrov classification scheme. The space-time develops circular closed timelike curves everywhere outside a finite region of space i.e., beyond a null curve. Furthermore, the physical interpretation of the solution based on the study of the equations of geodesic deviation is presented. Finally, the von Zeipel cylinders with respect to the Zero Angular Momentum Observers (ZAMOs) is discussed. In addition, circular null and timelike geodesic of pace-time are also presented.

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REFERENCES

  1. T. Lewis, Proc. Roy. Soc. Lond. A 136, 176 (1932).

    Article  ADS  Google Scholar 

  2. W. J. van Stockum, Proc. R. Soc. Edin. 57, 135 (1937).

  3. F. J. Tipler, Phys. Rev. D 9, 2203 (1974).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. R. Kerr, Phys. Rev. Lett. 11, 237 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  6. M. S. Morris, K. S. Thorne, and U. Yurtsever, Phys. Rev. Lett. 61, 1446 (1988).

    Article  ADS  Google Scholar 

  7. M. S. Morris and K. S. Thorne, Am. J. Phys. 56, 395 (1988).

    Article  ADS  Google Scholar 

  8. B. Jensen and H. H. Soleng, Phys. Rev. D 45, 3528 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  9. J. R. Gott, Phys. Rev. Lett. 66, 1126 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  10. S. V. Krasnikov, Class. Quantum Grav. 15, 997 (1998).

    Article  ADS  Google Scholar 

  11. A. Ori, Phys. Rev. Lett. 95, 021101 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  12. W. B. Bonnor and B. R. Steadman, Gen. Rel. Grav. 37, 1833 (2005).

    Article  ADS  Google Scholar 

  13. D. Sarma, M. Patgiri, and F. U. Ahmed, Gen. Rel. Grav. 46, 1633 (2014).

    Article  ADS  Google Scholar 

  14. F. Ahmed, B. B. Hazarika, and D. Sarma, EPJ Plus 131, 230 (2016).

    Google Scholar 

  15. F. Ahmed, Ann. Phys. (N.Y.) 382, 127 (2017).

    Article  ADS  Google Scholar 

  16. F. Ahmed, Ann. Phys. (N. Y.) 386, 25 (2017).

    Article  ADS  Google Scholar 

  17. F. Ahmed, Commun. Theor. Phys. 67, 189 (2017).

    Article  ADS  Google Scholar 

  18. F. Ahmed, Commun. Theor. Phys. 68, 735 (2017).

    Article  ADS  Google Scholar 

  19. F. Ahmed, Prog. Theor. Exp. Phys. 2017, 043E02 (2017).

  20. F. Ahmed, Prog. Theor. Exp. Phys. 2017, 083E03 (2017).

  21. D. Sarma, F. Ahmed, and M. Patgiri, Adv. High Energy Phys. 2016, 2546186 (2016).

    Article  Google Scholar 

  22. F. Ahmed, Adv. High Energy Phys. 2017, 3587018 (2017).

    Google Scholar 

  23. F. Ahmed, Adv. High Energy Phys. 2017, 7943649 (2017).

    Google Scholar 

  24. F. Ahmed, Int. J. Geom. Meths. Mod. Phys. 15, 1850153 (2018).

    Article  Google Scholar 

  25. F. Ahmed, Theor. Math. Phys. 195, 916 (2018).

    Article  Google Scholar 

  26. F. Ahmed, J. Phys. Commun. 2, 035036 (2018).

    Article  Google Scholar 

  27. F. Ahmed, Eur. Phys. J. C 78 (5), 385 (2018).

    Article  ADS  Google Scholar 

  28. F. Ahmed, Prog. Theor. Exp. Phys. 2019, 013E03 (2019).

  29. F. Ahmed, Grav. Cosmol. 26 (2), 136 (2020).

    Article  ADS  Google Scholar 

  30. B. Carter, Commun. Math. Phys. 17, 233 (1970).

    Article  ADS  Google Scholar 

  31. M. Mars and J. M. M. Senovilla, Class. Quantum Grav. 10, 1633 (1993).

    Article  ADS  Google Scholar 

  32. J. Carot, J. M. M. Senovilla, and R. Vera, Class. Quantum Grav. 16 3025 (1999).

    Article  ADS  Google Scholar 

  33. A. Barnes, Class. Quantum Grav. 17, 2605 (2001).

    Article  ADS  Google Scholar 

  34. A. Barnes, Class. Quantum Grav. 18, 5511 (2001).

    Article  ADS  Google Scholar 

  35. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions to Einstein’s Field Equations (Cambridge University Press, Cambridge, 2003).

    Book  MATH  Google Scholar 

  36. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Spacetime (Cambridge University Press, Cambridge, 1973).

    Book  MATH  Google Scholar 

  37. J. B. Griffiths and J. Podolsky, Exact Space-Times in General Relativity (Cambridge University Press, Cambridge 2009).

    Book  MATH  Google Scholar 

  38. V. M. Rosa and P. S. Letelier, gr-qc/0706.3212.

  39. V. M. Rosa and P. S. Letelier, Gen. Rel. Grav. 39, 1419 (2007).

    Article  ADS  Google Scholar 

  40. V. M. Rosa and P. S. Letelier, Phys. Lett. A 370, 99 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  41. J. Bic̆ák and J. Podolský, J. Math. Phys. 40, 4506 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  42. J. Podolský and M. Ortaggio, Class. Quantum Grav. 20, 1685 (2003).

    Article  ADS  Google Scholar 

  43. M. A. Abramowicz, Acta Astronomica 21, 81 (1971).

    ADS  Google Scholar 

  44. M. A. Abramowicz, Acta Astronomica 24, 45 (1974).

    ADS  Google Scholar 

  45. M. A. Abramowicz, J. C. Miller and Z. Stuchlík, Phys. Rev. D 47, 1440 (1993).

    Article  ADS  Google Scholar 

  46. P. Collas and D. Klein, Gen. Rel. Grav. 36, 1197 (2004).

    Article  ADS  Google Scholar 

  47. H. T. Mei and W. Y. Jiu, Chinese Physics 15, 232 (2006).

    Article  ADS  Google Scholar 

  48. M. A. Abramowicz, P. Nurowski, and N. Wex, Class. Quantum Grav. 12, 1467 (1995).

    Article  ADS  Google Scholar 

  49. P. I. Jefremov and V. Perlick, Class. Quantum Grav. 33, 245014 (2016).

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENT

The author sincerely acknowledges the anonymous kind referee for his/her valuable comments and suggestions.

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  1. Ajmal College of Arts and Science, Assam, Dhubri-783324, India

    Faizuddin Ahmed

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  1. Faizuddin Ahmed
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Ahmed, F. Axially Symmetric Type N Space-Time with Causality Violating Curves and the von Zeipel Cylinder. Gravit. Cosmol. 26, 265–272 (2020). https://doi.org/10.1134/S0202289320030020

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  • DOI: https://doi.org/10.1134/S0202289320030020

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