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Axially symmetric static sources: A general framework and some analytical solutions

L. Herrera*, A. Di Prisco†, and J. Ibáñez‡

J. Ospino§

  • Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco, Bilbao 48993, Spain

  • Departamento de Matemática Aplicada, Universidad de Salamanca, Salamanca 37007, Spain

  • *Also at U.C.V., Caracas. laherrera@cantv.net.ve
  • †Also at U.C.V., Caracas. adiprisc@fisica.ciens.ucv.ve
  • ‡j.ibanez@ehu.es
  • §jhozcrae@usal.es
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Phys. Rev. D 87, 024014 – Published 8 January, 2013

DOI: https://doi.org/10.1103/PhysRevD.87.024014

Abstract

We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed with axial symmetry. The structure scalars are calculated and the inhomogeneity factors are identified. Finally some exact analytical solutions were found. One of these solutions describes an incompressible spheroid with isotropic pressure and becomes the well-known interior Schwarzschild solution in the spherically symmetric limit; however, it cannot be matched smoothly to any Weyl exterior metric. Another family of solutions was found that corresponds to an anisotropic fluid distribution and can in principle be matched to a Weyl exterior.

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References (47)

  1. W. Israel, Phys. Rev. 164, 1776 (1967).
  2. H. Weyl, Ann. Phys. (Berlin) 54, 117 (1918).
  3. H. Weyl, Ann. Phys. (Berlin) 364, 185 (1919).
  4. T. Levi-Civita, Atti Accad. Naz. Lincei Cl Sci. Fis., Mat. Nat., Rend 28, 101 (1919).
  5. J. L. Synge, Relativity, the General Theory (North-Holland, Amsterdam, 1960).
  6. J. Winicour, A. I. Janis, and E. T. Newman, Phys. Rev. 176, 1507 (1968).
  7. A. Janis, E. T. Newman, and J. Winicour, Phys. Rev. Lett. 20, 878 (1968).
  8. L. Bel, Gen. Relativ. Gravit. 1, 337 (1971).
  9. F. I. Cooperstock and G. J. Junevicus, Nuovo Cimento Soc. Ital. Fis. B 16, 387 (1973).
  10. L. Herrera, Int. J. Mod. Phys. D 17, 557 (2008).
  11. L. Herrera, Int. J. Mod. Phys. D 17, 2507 (2008).
  12. W. C. Hernandez, Jr., Phys. Rev. 153, 1359 (1967).
  13. B. W. Stewart, D. Papadopoulos, L. Witten, R. Berezdivin, and L. Herrera, Gen. Relativ. Gravit. 14, 97 (1982).
  14. L. Herrera, G. Magli, and D. Malafarina, Gen. Relativ. Gravit. 37, 1371 (2005).
  15. L. Herrera, W. Barreto, and J. L. Hernández-Pastora, Gen. Relativ. Gravit. 37, 873 (2005).
  16. J. J. J. Marek, Phys. Rev. 163, 1373 (1967).
  17. K. Y. Fu, Astrophys. J. 190, 411 (1974).
  18. H. Ardavan and M. Hossein Partovi, Phys. Rev. D 16, 1664 (1977).
  19. W. B. Bonnor, An Interior Solution for the Curzon Body, (to be published).
  20. L. Herrera, J. Ospino, A. Di Prisco, E. Fuenmayor, and O. Troconis, Phys. Rev. D 79, 064025 (2009).
  21. L. Herrera, A. Di Prisco, J. Ospino, and J. Carot, Phys. Rev. D 82, 024021 (2010).
  22. L. Herrera, A. Di Prisco, and J. Ospino, Gen. Relativ. Gravit. 42, 1585 (2010).
  23. L. Herrera, A. Di Prisco, and J. Ibáñez, Phys. Rev. D 84, 064036 (2011).
  24. L. Herrera, A. Di Prisco, and J. Ibáñez, Phys. Rev. D 84, 107501 (2011).
  25. L. Herrera, A. Di Prisco, and J. Ospino, Gen. Relativ. Gravit. 44, 2645 (2012).
  26. M. Sharif and M. Zaeem Ul Haq Bhatti, Gen. Relativ. Gravit. 44, 2811 (2012).
  27. M. Sharif and M. Zaeem Ul Haq Bhatti, Mod. Phys. Lett. A 27, 1250141 (2012).
  28. H. Bondi, Proc. R. Soc. A 281, 39 (1964).
  29. G. F. R. Ellis, in Relativistic Cosmology, Proceedings of the International School of Physics “Enrico Fermi,” Course 47: General Relativity and Cosmology, edited by R. K. Sachs (Academic Press, New York, 1971).
  30. G. F. R. Ellis, Gen. Relativ. Gravit. 41, 581 (2009).
  31. L. Herrera, Int. J. Mod. Phys. D 20, 1689 (2011).
  32. A. K. M. Masood-ul-Alama, Gen. Relativ. Gravit. 39, 55 (2007).
  33. F. Pacini, Nature (London) 216, 567 (1967).
  34. T. Gold, Nature (London) 218, 731 (1968).
  35. J. P. Ostriker and J. E. Gunn, Astrophys. J. 157, 1395 (1969).
  36. J. C. Kemp, J. B. Swedlund, J. D. Landstreet, and J. R. P. Angel, Astrophys. J. 161, L77 (1970).
  37. G. D. Schmidt and P. S. Smith, Astrophys. J. 448, 305 (1995).
  38. A. Putney, Astrophys. J. 451, L67 (1995).
  39. D. Reimers, S. Jordan, D. Koester, N. Bade, Th. Kohler, and L. Wisotzki, Astron. Astrophys. 311, 572 (1996).
  40. V. Canuto and H. Y. Chiu, Phys. Rev. 173, 1210 (1968).
  41. M. Chaichian, S. S. Masood, C. Montone, A. Pérez-Martinez, and H. Pérez Rojas, Phys. Rev. Lett. 84, 5261 (2000).
  42. A. Pérez-Martinez, H. Pérez Rojas, and H. J. Mosquera Cuesta, Int. J. Mod. Phys. D 17, 2107 (2008).
  43. E. J. Ferrera, V. de la Incera, J. P. Keith, I. Portillo, and P. L. Springsteen, Phys. Rev. C 82, 065802 (2010).
  44. R. González Felipe and A. Pérez-Martinez, J. Phys. G 36, 075202 (2009).
  45. M. Sinha, B. Mukhopadhyay, and A. Sedrakian, arXiv:1005.4995.
  46. U. Das and B. Mukhopadhyay, Int. J. Mod. Phys. D 21, 1242001 (2012).
  47. L. Herrera and N. O. Santos, Phys. Rep. 286, 53 (1997).

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Phys. Rev. D 87, 024014– Published 8 January, 2013
  • Received 19 November 2012

© 2013 American Physical Society

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