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Advances in High Energy Physics
Volume 2016, Article ID 2546186, 4 pages
http://dx.doi.org/10.1155/2016/2546186
Research Article

Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

Department of Physics, Cotton College, Guwahati 781001, India

Received 17 August 2016; Revised 13 October 2016; Accepted 13 October 2016

Academic Editor: Luis A. Anchordoqui

Copyright © 2016 Debojit Sarma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. R. Penrose, “The question of cosmic censorship,” in Black Holes and Relativistic Stars, R. M. Wald, Ed., chapter 5, The Chicago University Press, Chicago, Ill, USA, 1998. View at Google Scholar
  2. R. M. Wald, “Gravitational collapse and cosmic censorship,” https://arxiv.org/abs/gr-qc/9710068.
  3. P. S. Joshi and D. Malafarina, “Recent developments in gravitational collapse and spacetime singularities,” International Journal of Modern Physics D, vol. 20, no. 14, p. 2641, 2011. View at Publisher · View at Google Scholar
  4. K. S. Virbhadra, D. Narasimha, and S. M. Chitre, “Role of the scalar field in gravitational lensing,” Astronomy and Astrophysics, vol. 337, no. 1, pp. 1–8, 1998. View at Google Scholar · View at Scopus
  5. K. S. Virbhadra and G. F. Ellis, “Gravitational lensing by naked singularities,” Physical Review D, vol. 65, no. 10, Article ID 103004, 2002. View at Publisher · View at Google Scholar
  6. G. N. Gyulchev and S. S. Yazadjiev, “Gravitational lensing by rotating naked singularities,” Physical Review D, vol. 78, no. 8, Article ID 083004, 2008. View at Publisher · View at Google Scholar
  7. M. C. Werner and A. O. Petters, “Magnification relations for Kerr lensing and testing cosmic censorship,” Physical Review D, vol. 76, no. 6, Article ID 064024, 6 pages, 2007. View at Publisher · View at Google Scholar
  8. C. Bambi and N. Yoshida, “Shape and position of the shadow in the δ=2 Tomimatsu–Sato spacetime,” Classical and Quantum Gravity, vol. 27, no. 20, Article ID 205006, 2010. View at Publisher · View at Google Scholar
  9. C. Bambi and K. Freese, “Apparent shape of super-spinning black holes,” Physical Review D. Particles, Fields, Gravitation, and Cosmology, vol. 79, no. 4, Article ID 043002, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. K. Hioki and K.-I. Maeda, “Measurement of the Kerr spin parameter by observation of a compact object's shadow,” Physical Review D, vol. 80, Article ID 024042, 2009. View at Publisher · View at Google Scholar
  11. A. N. Chowdhury, M. Patil, D. Malafarina, and P. Joshi, “Circular geodesics and accretion disks in the Janis-Newman-Winicour and gamma metric spacetimes,” Physical Review D, vol. 85, no. 10, Article ID 104031, 2012. View at Publisher · View at Google Scholar
  12. K. Gödel, “An example of a new type of cosmological solutions of Einstein's field equations of gravitation,” Reviews of Modern Physics, vol. 21, pp. 447–450, 1949. View at Publisher · View at Google Scholar · View at MathSciNet
  13. W. J. van Stockum, “The gravitational field of a distribution of particles rotating about an axis of symmetry,” Proceedings of the Royal Society of Edinburgh, vol. 57, pp. 135–154, 1937. View at Google Scholar
  14. F. J. Tipler, “Rotating cylinders and the possibility of global causality violation,” Physical Review D, vol. 9, pp. 2203–2206, 1974. View at Publisher · View at Google Scholar · View at MathSciNet
  15. P. Collas and D. Klein, “Letter: causality violating geodesics in bonnor's rotating dust metric,” General Relativity and Gravitation, vol. 36, no. 11, pp. 2549–2557, 2004. View at Publisher · View at Google Scholar
  16. I. R. Gott, “Closed timelike curves produced by pairs of moving cosmic strings: exact solutions,” Physical Review Letters, vol. 66, no. 9, pp. 1126–1129, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  17. M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,” Physical Review Letters, vol. 61, no. 13, pp. 1446–1449, 1988. View at Publisher · View at Google Scholar · View at Scopus
  18. D. Sarma, M. Patgiri, and F. U. Ahmed, “Pure radiation metric with stable closed timelike curves,” General Relativity and Gravitation, vol. 46, article 1633, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. L. A. Anchordoqui, S. E. P. Bergliaffa, M. L. Trobo, and G. S. Birman, “Cylindrically symmetric spinning Brans-Dicke space-times with closed timelike curves,” Modern Physics Letters A, vol. 14, no. 17, pp. 1105–1111, 1999. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Ori, “Formation of closed timelike curves in a composite vacuum/dust asymptotically flat spacetime,” Physical Review D. Particles, Fields, Gravitation, and Cosmology, vol. 76, no. 4, Article ID 044002, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  21. A. Ori, “A class of time-machine solutions with a compact vacuum core,” Physical Review Letters, vol. 95, no. 2, Article ID 021101, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  22. Y. Soen and A. Ori, “Improved time-machine model,” Physical Review D, vol. 54, no. 8, pp. 4858–4861, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  23. A. Ori and Y. Soen, “Causality violation and the weak energy condition,” Physical Review D, vol. 49, no. 8, pp. 3990–3997, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. I. D. Soares, “Inhomogeneous rotating universes with closed timelike geodesics of matter,” Journal of Mathematical Physics, vol. 21, no. 3, pp. 521–525, 1980. View at Publisher · View at Google Scholar
  25. W. B. Bonnor and B. R. Steadman, “Exact solutions of the Einstein-Maxwell equations with closed timelike curves,” General Relativity and Gravitation, vol. 37, no. 11, pp. 1833–1844, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. Ø. Grøn and S. Johannesen, “Closed timelike geodesics in a gas of cosmic strings,” New Journal of Physics, vol. 10, Article ID 103025, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. Ø. Grøn and S. Johannesen, “A spacetime with closed timelike geodesics everywhere,” Nuovo Cimento della Societa Italiana di Fisica B, vol. 125, no. 10, pp. 1215–1221, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. D. Sarma, M. Patgiri, and F. U. Ahmed, “A vacuum spacetime with closed null geodesics,” Annals of Physics, vol. 329, pp. 179–184, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. M. Mars and J. M. M. Senovilla, “Axial symmetry and conformal Killing vectors,” Classical and Quantum Gravity, vol. 10, no. 8, pp. 1633–1647, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. M. Mars and J. M. M. Senovilla, “Comment on ‘an infinite perfect fluid in cylindrically symmetric steady differential rotation’,” Classical and Quantum Gravity, vol. 12, p. 2071, 1995. View at Publisher · View at Google Scholar
  31. W. Kinnersley, “Type D vacuum metrics,” Journal of Mathematical Physics, vol. 10, pp. 1195–1203, 1969. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions to Einstein's Field Equations, Cambridge University Press, Cambridge, UK, 2003.
  33. C. W. Misner, “Taub-nut space as a counterexample to almost anything,” in Relativity Theory and Astrophysics I: Relativity and Cosmology, J. Ehlers, Ed., vol. 8 of Lectures in Applied Mathematics, American Mathematical Society, 1967. View at Google Scholar
  34. K. Gödel, “An example of a new type of cosmological solutions of Einstein's field equations of gravitation,” Reviews of Modern Physics, vol. 21, no. 3, pp. 447–450, 1949. View at Publisher · View at Google Scholar · View at MathSciNet
  35. C. J. Clarke and F. de Felice, “Globally noncausal space-times. II. Naked singularities and curvature conditions,” General Relativity and Gravitation, vol. 16, no. 2, pp. 139–148, 1984. View at Publisher · View at Google Scholar
  36. F. de Felice, “Cosmic time machines: the causality issue,” EPJ Web of Conferences, vol. 58, Article ID 01001, 4 pages, 2013. View at Publisher · View at Google Scholar