General Relativity and Gravitation

, Volume 44, Issue 10, pp 2645–2667 | Cite as

Cylindrically symmetric relativistic fluids: a study based on structure scalars

Research Article

Abstract

Applying the 1 + 3 formalism we write down the full set of equations governing the structure and the evolution of self-gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, in terms of scalar quantities obtained from the orthogonal splitting of the Riemann tensor (structure scalars), in the context of general relativity. These scalars which have been shown previously (in the spherically symmetric case) to be related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux, active gravitational mass etc, are shown here to play also a very important role in the dynamics of cylindrically symmetric fluids. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through three of these scalars.

Keywords

Relativistic fluids Cylindrically symmetric systems Dissipative fluids Causal dissipative theories 

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References

  1. 1.
    Herrera L., Ospino J., Di Prisco A., Fuenmayor E., Troconis O.: Phys. Rev. D 79, 064025 (2009)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Herrera L., Di Prisco A., Ospino J., Carot J.: Phys. Rev. D 82, 024021 (2010)ADSCrossRefGoogle Scholar
  3. 3.
    Herrera L., Di Prisco A., Ospino J.: Gen. Relativ. Gravit. 42, 1585 (2010)MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    Herrera L., Di Prisco A., Ibáñez J.: Phys. Rev. D 84, 064036 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    Herrera L., Di Prisco A., Ibáñez J.: Phys. Rev. D 84, 107501 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    Thorne K.S.: Phy. Rev. 138, B251 (1965)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Cocke W.J.: J. Math. Phys. 7, 1171 (1966)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Apostolatos T.A., Thorne K.S.: Phys. Rev. D 46, 2435 (1992)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Tod P., Mena F.: Phys. Rev. D 70, 104028 (2004)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Bonnor W.B.: Class. Quantum Grav. 22, 803 (2005)MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    Konkowski D., Heliwell T.: Gen. Relativ. Gravit. 38, 1069 (2006)ADSMATHCrossRefGoogle Scholar
  12. 12.
    Sobreira A., de Marques G.A., Fonseca-Neto J., Bezerra V.: J. Math. Phys. 50, 052502 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    Ponce de León J.: Mod. Phys. Lett. A 24, 1659 (2009)ADSMATHCrossRefGoogle Scholar
  14. 14.
    Di Prisco A., Herrera L., MacCallum M.A.H., Santos N.O.: Phys. Rev. D 80, 064031 (2009)MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Krisch J.P., Glass E.N.: J. Math. Phys. 52, 052503 (2011)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    MacCallum M.A.H.: Gen. Relativ. Gravit. 43, 2297 (2011)MathSciNetADSMATHCrossRefGoogle Scholar
  17. 17.
    Sharif M., Abbas G.: Astrophys. Space. Sci. 335, 515 (2011)ADSMATHCrossRefGoogle Scholar
  18. 18.
    Trendafilova C.S., Fulling S.A.: Eur. J. Phys. 32, 1663 (2011)CrossRefGoogle Scholar
  19. 19.
    Sharif M., Abbas G.: J. Phys. Soc. Jpn. 80, 104002 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    Ellis G.F.R.: Relativistic Cosmology. In: Sachs, R.K. (ed) Proceedings of the International School of Physics “ Enrico Fermi”, Course 47: General Relativity and Cosmology, Academic Press, New York and London (1971)Google Scholar
  21. 21.
    Ellis G.F.R.: Gen. Relativ. Gravit. 41, 581 (2009)ADSMATHCrossRefGoogle Scholar
  22. 22.
    Ehlers J.: Gen. Relativ. Gravit. 25, 1225 (1993)MathSciNetADSMATHCrossRefGoogle Scholar
  23. 23.
    Ellis G.F.R.: Cosmological models (Cargèse Lectures 1998). NATO Adv. Study Inst. Ser C Math. Phys. Sci. 541, 1 (1999)Google Scholar
  24. 24.
    Tsagas C.G., Challinor A., Maartens R.: Phys. Rep. 465, 61 (2008)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    Bel L.: Ann. Inst. H Poincaré 17, 37 (1961)MathSciNetMATHGoogle Scholar
  26. 26.
    García-Parrado Gómez Lobo A.: Class. Quantum Grav. 25, 015006 (2008)CrossRefGoogle Scholar
  27. 27.
    van Elst H., Uggla C.: Class. Quantum Grav. 14, 2673 (1997)ADSMATHCrossRefGoogle Scholar
  28. 28.
    Herrera L., Santos N.O., Carot J.: J. Math. Phys. 47, 052502 (2006)MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    Herrera L., Barreto W., Carot J., Di Prisco A.: Class. Quantum Grav. 24, 2645 (2007)MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    Herrera L., Di Prisco A., Martín J., Ospino J., Santos N.O., Troconis O.: Phys. Rev. D 69, 084026 (2004)ADSCrossRefGoogle Scholar
  31. 31.
    Müller I.: Z. Physik 198, 329 (1967)ADSMATHCrossRefGoogle Scholar
  32. 32.
    Israel W.: Ann. Phys. (NY) 100, 310 (1976)MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    Israel W., Stewart J.: Phys. Lett. A 58, 213 (1976)ADSCrossRefGoogle Scholar
  34. 34.
    Israel W., Stewart J.: Ann. Phys. (NY) 118, 341 (1979)MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    Joseph D., Preziosi L.: Rev. Mod. Phys. 61, 41 (1989)MathSciNetADSMATHCrossRefGoogle Scholar
  36. 36.
    Jou D., Casas-Vázquez J., Lebon G.: Rep. Prog. Phys. 51, 1105 (1988)ADSCrossRefGoogle Scholar
  37. 37.
    Maartens, R.: astro-ph/9609119 Google Scholar
  38. 38.
    Herrera L., Pavón D.: Physica A 307, 121 (2002)ADSMATHCrossRefGoogle Scholar
  39. 39.
    Hiscock W., Lindblom L.: Ann. Phys. (NY) 151, 466 (1983)MathSciNetADSMATHCrossRefGoogle Scholar
  40. 40.
    Eckart C.: Phys. Rev. 58, 919 (1940)ADSCrossRefGoogle Scholar
  41. 41.
    Landau L., Lifshitz E.: Fluid Mechanics. Pergamon Press, London (1959)Google Scholar
  42. 42.
    Pavón D., Jou D., Casas-Vázquez J.: Ann. Inst. H Poincaré A 36, 79 (1982)Google Scholar
  43. 43.
    Carter, B.: In: Cahen,M., Debever, R., Geheniau, J. (eds.) Journées Relativistes., Université Libre de Bruxelles, Bruxelles (1976)Google Scholar
  44. 44.
    Cattaneo C.: Atti Semin. Mat. Fis. Univ. Modena 3, 3 (1948)Google Scholar
  45. 45.
    Andersson N., Lopez-Monsalvo C.: Class. Quantum Grav. 28, 195023 (2011)MathSciNetADSCrossRefGoogle Scholar
  46. 46.
    Herrera L., Santos N.O.: Mon. Not. R. Astr. Soc. 287, 161 (1997)ADSGoogle Scholar
  47. 47.
    Herrera L., Di Prisco A., Hernández-Pastora J., Martín J., Martínez J.: Class. Quantum Grav. 14, 2239 (1997)ADSMATHCrossRefGoogle Scholar
  48. 48.
    Herrera L.: Phys. Lett. A 300, 157 (2002)ADSMATHCrossRefGoogle Scholar
  49. 49.
    Herrera L., Santos N.O.: Phys. Rev. D 70, 084004 (2004)MathSciNetADSCrossRefGoogle Scholar
  50. 50.
    Herrera L., Di Prisco A., Barreto W.: Phys. Rev. D 73, 024008 (2006)ADSCrossRefGoogle Scholar
  51. 51.
    Herrera L.: Int. J. of Mod. Phys. D 15, 2197 (2006)MathSciNetADSMATHCrossRefGoogle Scholar
  52. 52.
    Di Prisco A., Herrera L., Le Denmat G., MacCallum M.A.H., Santos N.O.: Phys. Rev. D 76, 064017 (2007)ADSCrossRefGoogle Scholar
  53. 53.
    Herrera L., Di Prisco A., Fuenmayor E., Troconis O.: Int. J. Mod. Phys. D 18, 129 (2009)ADSMATHCrossRefGoogle Scholar
  54. 54.
    Sharif M., Rehmat Z.: Gen. Relativ. Gravit. 42, 1795 (2010)MathSciNetADSMATHCrossRefGoogle Scholar
  55. 55.
    Sharif M., Siddiqa A.: Gen. Relativ. Gravit. 43, 73 (2011)MathSciNetADSMATHCrossRefGoogle Scholar
  56. 56.
    Glass E.N.: J. Math. Phys. 16, 2361 (1975)MathSciNetADSMATHCrossRefGoogle Scholar
  57. 57.
    Herrera L.: Int. J. Mod. Phys. D 20, 1689 (2011)MathSciNetADSCrossRefGoogle Scholar
  58. 58.
    Herrera L., Le Denmat G., Marcilhacy G., Santos N.O.: Int. J. Mod. Phys. D 14, 657 (2005)MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Departamento de Física Teórica e Historia de la CienciaUniversidad del País VascoCaracasVenezuela
  2. 2.U.C.V.CaracasVenezuela
  3. 3.Departamento de Matemática AplicadaUniversidad de SalamancaSalamancaSpain

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