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Cylindrically symmetric relativistic fluids: a study based on structure scalars

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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.

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References

  1. Herrera L., Ospino J., Di Prisco A., Fuenmayor E., Troconis O.: Phys. Rev. D 79, 064025 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  2. Herrera L., Di Prisco A., Ospino J., Carot J.: Phys. Rev. D 82, 024021 (2010)

    Article  ADS  Google Scholar 

  3. Herrera L., Di Prisco A., Ospino J.: Gen. Relativ. Gravit. 42, 1585 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Herrera L., Di Prisco A., Ibáñez J.: Phys. Rev. D 84, 064036 (2011)

    Article  ADS  Google Scholar 

  5. Herrera L., Di Prisco A., Ibáñez J.: Phys. Rev. D 84, 107501 (2011)

    Article  ADS  Google Scholar 

  6. Thorne K.S.: Phy. Rev. 138, B251 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  7. Cocke W.J.: J. Math. Phys. 7, 1171 (1966)

    Article  MathSciNet  ADS  Google Scholar 

  8. Apostolatos T.A., Thorne K.S.: Phys. Rev. D 46, 2435 (1992)

    Article  MathSciNet  Google Scholar 

  9. Tod P., Mena F.: Phys. Rev. D 70, 104028 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  10. Bonnor W.B.: Class. Quantum Grav. 22, 803 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Konkowski D., Heliwell T.: Gen. Relativ. Gravit. 38, 1069 (2006)

    Article  ADS  MATH  Google Scholar 

  12. Sobreira A., de Marques G.A., Fonseca-Neto J., Bezerra V.: J. Math. Phys. 50, 052502 (2006)

    Article  ADS  Google Scholar 

  13. Ponce de León J.: Mod. Phys. Lett. A 24, 1659 (2009)

    Article  ADS  MATH  Google Scholar 

  14. Di Prisco A., Herrera L., MacCallum M.A.H., Santos N.O.: Phys. Rev. D 80, 064031 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  15. Krisch J.P., Glass E.N.: J. Math. Phys. 52, 052503 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  16. MacCallum M.A.H.: Gen. Relativ. Gravit. 43, 2297 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Sharif M., Abbas G.: Astrophys. Space. Sci. 335, 515 (2011)

    Article  ADS  MATH  Google Scholar 

  18. Trendafilova C.S., Fulling S.A.: Eur. J. Phys. 32, 1663 (2011)

    Article  Google Scholar 

  19. Sharif M., Abbas G.: J. Phys. Soc. Jpn. 80, 104002 (2011)

    Article  ADS  Google Scholar 

  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. Ellis G.F.R.: Gen. Relativ. Gravit. 41, 581 (2009)

    Article  ADS  MATH  Google Scholar 

  22. Ehlers J.: Gen. Relativ. Gravit. 25, 1225 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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. Tsagas C.G., Challinor A., Maartens R.: Phys. Rep. 465, 61 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  25. Bel L.: Ann. Inst. H Poincaré 17, 37 (1961)

    MathSciNet  MATH  Google Scholar 

  26. García-Parrado Gómez Lobo A.: Class. Quantum Grav. 25, 015006 (2008)

    Article  Google Scholar 

  27. van Elst H., Uggla C.: Class. Quantum Grav. 14, 2673 (1997)

    Article  ADS  MATH  Google Scholar 

  28. Herrera L., Santos N.O., Carot J.: J. Math. Phys. 47, 052502 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  29. Herrera L., Barreto W., Carot J., Di Prisco A.: Class. Quantum Grav. 24, 2645 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Herrera L., Di Prisco A., Martín J., Ospino J., Santos N.O., Troconis O.: Phys. Rev. D 69, 084026 (2004)

    Article  ADS  Google Scholar 

  31. Müller I.: Z. Physik 198, 329 (1967)

    Article  ADS  MATH  Google Scholar 

  32. Israel W.: Ann. Phys. (NY) 100, 310 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  33. Israel W., Stewart J.: Phys. Lett. A 58, 213 (1976)

    Article  ADS  Google Scholar 

  34. Israel W., Stewart J.: Ann. Phys. (NY) 118, 341 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  35. Joseph D., Preziosi L.: Rev. Mod. Phys. 61, 41 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. Jou D., Casas-Vázquez J., Lebon G.: Rep. Prog. Phys. 51, 1105 (1988)

    Article  ADS  Google Scholar 

  37. Maartens, R.: astro-ph/9609119

  38. Herrera L., Pavón D.: Physica A 307, 121 (2002)

    Article  ADS  MATH  Google Scholar 

  39. Hiscock W., Lindblom L.: Ann. Phys. (NY) 151, 466 (1983)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Eckart C.: Phys. Rev. 58, 919 (1940)

    Article  ADS  Google Scholar 

  41. Landau L., Lifshitz E.: Fluid Mechanics. Pergamon Press, London (1959)

    Google Scholar 

  42. Pavón D., Jou D., Casas-Vázquez J.: Ann. Inst. H Poincaré A 36, 79 (1982)

    Google Scholar 

  43. Carter, B.: In: Cahen,M., Debever, R., Geheniau, J. (eds.) Journées Relativistes., Université Libre de Bruxelles, Bruxelles (1976)

  44. Cattaneo C.: Atti Semin. Mat. Fis. Univ. Modena 3, 3 (1948)

    Google Scholar 

  45. Andersson N., Lopez-Monsalvo C.: Class. Quantum Grav. 28, 195023 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  46. Herrera L., Santos N.O.: Mon. Not. R. Astr. Soc. 287, 161 (1997)

    ADS  Google Scholar 

  47. Herrera L., Di Prisco A., Hernández-Pastora J., Martín J., Martínez J.: Class. Quantum Grav. 14, 2239 (1997)

    Article  ADS  MATH  Google Scholar 

  48. Herrera L.: Phys. Lett. A 300, 157 (2002)

    Article  ADS  MATH  Google Scholar 

  49. Herrera L., Santos N.O.: Phys. Rev. D 70, 084004 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  50. Herrera L., Di Prisco A., Barreto W.: Phys. Rev. D 73, 024008 (2006)

    Article  ADS  Google Scholar 

  51. Herrera L.: Int. J. of Mod. Phys. D 15, 2197 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. Di Prisco A., Herrera L., Le Denmat G., MacCallum M.A.H., Santos N.O.: Phys. Rev. D 76, 064017 (2007)

    Article  ADS  Google Scholar 

  53. Herrera L., Di Prisco A., Fuenmayor E., Troconis O.: Int. J. Mod. Phys. D 18, 129 (2009)

    Article  ADS  MATH  Google Scholar 

  54. Sharif M., Rehmat Z.: Gen. Relativ. Gravit. 42, 1795 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  55. Sharif M., Siddiqa A.: Gen. Relativ. Gravit. 43, 73 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. Glass E.N.: J. Math. Phys. 16, 2361 (1975)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  57. Herrera L.: Int. J. Mod. Phys. D 20, 1689 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  58. Herrera L., Le Denmat G., Marcilhacy G., Santos N.O.: Int. J. Mod. Phys. D 14, 657 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco, Caracas, Venezuela

    L. Herrera & A. Di Prisco

  2. U.C.V., Caracas, Venezuela

    L. Herrera & A. Di Prisco

  3. Departamento de Matemática Aplicada, Universidad de Salamanca, Salamanca, Spain

    J. Ospino

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  1. L. Herrera
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  2. A. Di Prisco
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  3. J. Ospino
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Correspondence to L. Herrera.

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Herrera, L., Di Prisco, A. & Ospino, J. Cylindrically symmetric relativistic fluids: a study based on structure scalars. Gen Relativ Gravit 44, 2645–2667 (2012). https://doi.org/10.1007/s10714-012-1422-8

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