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Advances in High Energy Physics
Volume 2017, Article ID 3587018, 7 pages
https://doi.org/10.1155/2017/3587018
Research Article

Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine

Hindustani Kendriya Vidyalaya, Dinesh Ojha Road, Guwahati 781005, India

Correspondence should be addressed to Faizuddin Ahmed; moc.liamg@51demhanidduziaf

Received 5 April 2017; Accepted 14 May 2017; Published 12 June 2017

Academic Editor: Torsten Asselmeyer-Maluga

Copyright © 2017 Faizuddin Ahmed. 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. E. Newman and R. Penrose, “An approach to gravitational radiation by a method of spin coefficients,” Journal of Mathematical Physics, vol. 3, pp. 566–578, 1962. View at Publisher · View at Google Scholar · View at MathSciNet
  2. E. Newman and R. Penrose, “Errata: an approach to gravitational radiation by a method of spin coefficients,” Journal of Mathematical Physics, vol. 4, 998 pages, 1963. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. Penrose, “Gravitational collapse: the role of general relativity,” Rivista del Nuovo Cimento, vol. 1, pp. 252–276, 1969. View at Google Scholar
  4. R. Penrose, “Singularities and time-asymetry,” in General Relativity: An Einstein Centenary Survey, S. W. Hawking and W. Israel, Eds., pp. 581–638, Cambridge University Press, Cambridge, 1979. View at Google Scholar · View at MathSciNet
  5. R. Penrose, “The question of cosmic censorship,” in Black Holes and Relativistic Stars, R. M. Wald, Ed., Chicago University Press, Chicago, Ill, USA, 1994. View at Google Scholar
  6. K. S. Virbhadra, D. Narasimha, and S. M. Chitre, “Role of scalar field in gravitational lensing,” Astronomy and Astrophysics, vol. 337, pp. 1–8, 1998. View at Google Scholar
  7. K. S. Virbhadra and G. F. R. Ellis, “Gravitational lensing by naked singularities,” Physical Review D, vol. 65, no. 10, Article ID 103004, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. G. N. Gyulchev and S. S. Yazadjiev, Physical Review D, vol. 78, Article ID 083004, 2008.
  9. M. Werner and A. Petters, “Magnification relations for Kerr lensing and testing cosmic censorship,” Physical Review D, vol. 76, Article ID 064024, 2007. View at Publisher · View at Google Scholar
  10. 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
  11. 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
  12. K. Hioki and K.-i. Maeda, “Bulk spacetimes for cosmological braneworlds with a time-dependent extra dimension,” Physical Review D, vol. 80, Article ID 024042, 2009. View at Publisher · View at Google Scholar
  13. 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, Article ID 104031, 2012. View at Publisher · View at Google Scholar
  14. G. Lemaitre, “L’univers en expansion,” Annales de la Societe Scientifique de Bruxelles A, vol. 53, p. 51, 1933. View at Google Scholar
  15. R. C. Tolman, “Effect of inhomogeneity on cosmological models,” Proceedings of the National Academy of Sciences of the United States of America, vol. 20, p. 169, 1934. View at Publisher · View at Google Scholar
  16. H. Bondi, “Spherically symmetrical models in general relativity,” Monthly Notices of the Royal Astronomical Society, vol. 107, p. 343, 1947. View at Publisher · View at Google Scholar · View at MathSciNet
  17. A. Papapetrou, A Random Walk in Relativity and Cosmology, Wiley, New York, NY, USA, 1985.
  18. P. C. Vaidya, “'Newtonian' Time in General Relativity,” Nature, vol. 171, pp. 260-261, 1953. View at Publisher · View at Google Scholar · View at MathSciNet
  19. D. Christodoulou, “Violation of cosmic censorship in the gravitational collapse of a dust cloud,” Communications in Mathematical Physics, vol. 93, pp. 171–195, 1984. View at Publisher · View at Google Scholar
  20. P. S. Joshi, Global Aspects in Gravitation and Cosmology, vol. 87 of International Series of Monographs on Physics, The Clarendon Press, Oxford, UK, 1993. View at MathSciNet
  21. P. S. Joshi, Singularities, Black Holes and Cosmic Censorship, IUCAA publication, Pune, India, 1997.
  22. S. S. Deshingkar, I. H. Dwivedi, and P. S. Joshi, “Physical nature of the central singularity in spherical collapse,” Physical Review D, vol. 59, Article ID 044018, 1999. View at Publisher · View at Google Scholar
  23. S. Barve, T. P. Singh, C. Vaz, and L. Witten, “A simple derivation of the naked singularity in spherical dust collapse,” Classical and Quantum Gravity, vol. 16, no. 6, pp. 1727–1732, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. P. S. Joshi and I. H. Dwivedi, “Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse,” Physical Review D, vol. 47, no. 12, pp. 5357–5369, 1993. View at Publisher · View at Google Scholar · View at Scopus
  25. P. S. Joshi and I. H. Dwivedi, “Initial data and the end state of spherically symmetric gravitational collapse,” Classical and Quantum Gravity, vol. 16, no. 1, pp. 41–59, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  26. K. S. Govinder and M. Govender, “Gravitational collapse of null radiation and a string fluid,” Physical Review D, vol. 68, no. 2, Article ID 024034, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  27. E. N. Glass and J. P. Krisch, “Radiation and string atmosphere for relativistic stars,” Physical Review D, vol. 57, p. 5945, 1998. View at Publisher · View at Google Scholar
  28. J. F. Villas da Rocha, “Type II fluid solutions to Einstein's field equations in N-dimensional spherical spacetimes,” International Journal of Modern Physics D, vol. 11, no. 1, pp. 113–124, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  29. L. Herrera, A. Di Prisco, and J. Ospino, “The space-time outside a source of gravitational radiation: the axially symmetric null fluid,” The European Physical Journal C, vol. 76, p. 603, 2016. View at Publisher · View at Google Scholar
  30. A. Krasinski, Inhomogeneous Cosmological Models, Cambridge University Press, Cambridge, 1997. View at Publisher · View at Google Scholar
  31. K. S. Thorne, Magic without Magic: John Archibald Wheeler, Freeman and Co., San Francisco, CA, USA, 1972.
  32. S. A. Hayward, “Gravitational waves, black holes and cosmic strings in cylindrical symmetry,” Classical and Quantum Gravity, vol. 17, p. 1749, 2000. View at Publisher · View at Google Scholar
  33. T. A. Apostolatos and K. S. Thorne, “Rotation halts cylindrical, relativistic gravitational collapse,” Physical Review. D. Third Series, vol. 46, no. 6, pp. 2435–2444, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. F. Echeverria, “Gravitational collapse of an infinite, cylindrical dust shell,” Physical Review D, vol. 47, no. 6, pp. 2271–2282, 1993. View at Publisher · View at Google Scholar · View at Scopus
  35. S. Guttia, T. P. Singh, P. A. Sundararaj, and C. Vaz, “Gravitational collapse of an infinite dust cylinder,” https://arxiv.org/abs/gr-qc/0212089.
  36. K.-I. Nakao and Y. Morisawa, “High speed dynamics of collapsing cylindrical dust fluid,” Classical and Quantum Gravity, vol. 21, no. 8, pp. 2101–2113, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  37. K. Nakao and Y. Morisawa, “High-speed cylindrical collapse of perfect fluid,” Progress of Theoretical Physics, vol. 113, p. 73, 2005. View at Google Scholar
  38. S. M. Goncalves and S. Jhingan, “A note on the cylindrical collapse of counter-rotating dust,” International Journal of Modern Physics. D. Gravitation, Astrophysics, Cosmology, vol. 11, no. 9, pp. 1469–1477, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  39. B. C. Nolan, “Naked singularities in cylindrical collapse of counterrotating dust shells,” Physical Review D, vol. 65, no. 10, Article ID 104006, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  40. P. R. C. T. Periera and A. Wang, “Gravitational collapse of cylindrical shells made of counterrotating dust particles,” Physical Review D, vol. 62, Article ID 124001, 2000. View at Publisher · View at Google Scholar
  41. A. Wang, “Critical collapse of a cylindrically symmetric scalar field in four-dimensional Einstein’s theory of gravity,” Physical Review D, vol. 68, no. 6, Article ID 064006, 12 pages, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  42. D. Sarma, F. Ahmed, and M. Patgiri, “Axially symmetric, asymptotically flat vacuum metric with a naked singularity and closed timelike curves,” Advances in High Energy Physics, vol. 2016, Article ID 2546186, 4 pages, 2016. View at Publisher · View at Google Scholar
  43. F. Ahmed, “Cylindrically symmetric, asymptotically flat, petrov type d spacetime with a naked curvature singularity and matter collapse,” Advances in High Energy Physics, vol. 2017, Article ID 7943649, 6 pages, 2017. View at Publisher · View at Google Scholar
  44. T. Chiba, “Cylindrically symmetric, asymptotically flat, petrov type D spacetime with a naked curvature singularity and matter collapse,” Progress of Theoretical Physics, vol. 95, p. 321, 1996. View at Google Scholar
  45. T. Piran, “Cylindrical general relativistic collapse,” Physical Review Letters, vol. 41, p. 1085, 1978. View at Publisher · View at Google Scholar
  46. K. S. Thorne, “Energy of infinitely long, cylindrically symmetric systems in general relativity,” Physical Review B, vol. 138, p. B251, 1965. View at Publisher · View at Google Scholar
  47. T. A. Morgan, General Relativity and Gravitation, vol. 4, no. 4, pp. 273–278, 1973. View at Publisher · View at Google Scholar
  48. P. S. Letelier and A. Z. Wang, “Singularities formed by the focusing of cylindrical null fluids,” Physical Review. D. Third Series, vol. 49, no. 10, pp. 5105–5110, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  49. J. M. Senovilla and R. Vera, “Cylindrically symmetric dust spacetime,” Classical and Quantum Gravity, vol. 17, no. 14, pp. 2843–2846, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  50. H. Bondi, “The mass of cylindrical systems in general relativity,” Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences, vol. 427, no. 1873, pp. 259–264, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  51. M. A. Melvin, “Pure magnetic and electric geons,” Physics Letters. B, vol. 8, pp. 65–68, 1964. View at Publisher · View at Google Scholar · View at MathSciNet
  52. M. A. Melvin, “Dynamics of Cylindrical Electromagnetic Universes,” Physical Review, vol. 139, p. B225, 1965. View at Publisher · View at Google Scholar
  53. J. C. de Araujo and A. Wang, “Rigidly rotating dust in general relativity,” General Relativity and Gravitation, vol. 32, no. 10, pp. 1971–1980, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  54. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein's Equations, Cambridge University Press, Cambridge, UK, 2003. View at MathSciNet
  55. Y. Kurita and K.-I. Nakao, “Naked singularity resolution in cylindrical collapse,” Physical Review. D. Third Series, vol. 73, no. 6, Article ID 064022, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  56. F. J. Tipler, “Singularities in conformally flat spacetimes,” Physics Letters A, vol. 64, no. 1, pp. 8–10, 1977. View at Publisher · View at Google Scholar · View at MathSciNet
  57. A. Krolak, “Towards the proof of the cosmic censorship hypothesis in cosmological space-times,” Journal of Mathematical Physics, vol. 28, no. 1, pp. 138–141, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  58. C. J. Clarke and A. Krolak, “Conditions for the occurrence of strong curvature singularities,” Journal of Geometry and Physics, vol. 2, no. 2, pp. 127–143, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  59. I. H. Dwivedi and P. S. Joshi, “On the nature of naked singularities in Vaidya spacetimes,” Classical and Quantum Gravity, vol. 6, no. 11, pp. 1599–1606, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  60. P. Collas and D. Klein, “Frame dragging anomalies for rotating bodies,” General Relativity and Gravitation, vol. 36, no. 5, pp. 1197–1206, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  61. H. T. Mei and W. Y. Jiu, “Frame dragging in the field of Kerr family,” Chinese Physics, vol. 15, no. 1, pp. 232–234, 2006. View at Publisher · View at Google Scholar · View at Scopus
  62. F. Ahmed, “Cylindrically symmetric pure radiation space-time and closed timelike geodesics,” Progress of Theoretical and Experimental Physics, vol. 2017, Article ID 043E02, 2017. View at Google Scholar
  63. 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
  64. S. W. Hawking, “Chronology protection conjecture,” Physical Review D, vol. 46, no. 2, pp. 603–611, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  65. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, London, UK, 1973. View at MathSciNet
  66. 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
  67. F. de Felice, Lecture Notes in Physics, vol. 455, Springer-Verlag Publishers, 1995.
  68. F. de Felice, “Naked singularities, cosmic time machines and impulsive events,” Nuovo Cimento B, vol. 122, p. 481, 2007. View at Google Scholar
  69. 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
  70. F. A. E. Pirani, “On the physical significance of the Riemann tensor,” Acta Physica Polonica. B, vol. 15, pp. 389–405, 1956. View at Google Scholar · View at MathSciNet
  71. F. A. E. Pirani, “Invariant formulation of gravitational radiation theory,” Physical Review, vol. 105, no. 3, pp. 1089–1099, 1957. View at Publisher · View at Google Scholar · View at Scopus
  72. P. Szekeres, “The gravitational compass,” Journal of Mathematical Physics, vol. 6, pp. 1387–1391, 1965. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  73. P. Szekeres, “On the propagation of gravitational fields in matter,” Journal of Mathematical Physics, vol. 7, p. 751, 1966. View at Google Scholar
  74. J. Bicák and J. Podolský, “Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of nontwisting type N solutions,” Journal of Mathematical Physics, vol. 40, no. 9, pp. 4506–4517, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  75. J. Podolský and M. Ortaggio, “Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes,” Classical and Quantum Gravity, vol. 20, no. 9, pp. 1685–1701, 2003. View at Publisher · View at Google Scholar · View at MathSciNet