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General magnetized Weyl solutions: disks and motion of charged particles

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Abstract

We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized spheroidal coordinates which is a generalization of the previous systems. The method used to build such solutions is the well-known complex potential formalism proposed by Ernst, using as seed solutions vacuum solutions of the Einstein field equations. We show explicitly some particular solutions among them a magnetized Erez-Rosen solution and a magnetized Morgan-Morgan solution, which we interpret as the exterior gravitational field of a finite dislike source immersed in a magnetic field. From them we also construct using the well known “displace, cut and reflect” method exact solutions representing relativistic thin disks of infinite extension. We then analyze the motion of electrically charged test particles around these fields for equatorial circular orbits and we discuss their stability against radial perturbations. For magnetized Morgan-Morgan fields we find that inside of disk the presence of magnetic field provides the possibility of to find relativist charged particles moving in both prograde and retrograde direction.

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References

  1. Lobanov A.P.: A&A 330, 79 (1998)

    ADS  Google Scholar 

  2. Aharonian F.A.: MNRAS 332, 215 (2002)

    Article  ADS  Google Scholar 

  3. Zakharov A.F. et al.: MNRAS 342, 1325 (2003)

    Article  ADS  Google Scholar 

  4. Greaves J.S. et al.: Nature 404, 732 (2000)

    Article  ADS  Google Scholar 

  5. Liu Y.T., Shapiro S.L., Stephens B.C.: Phys. Rev. D 76, 084017 (2007)

    Article  ADS  Google Scholar 

  6. Akiyama S. et al.: ApJ 584, 954 (2003)

    Article  ADS  Google Scholar 

  7. Vlemmings W.H.T., Diamond P.J., Imai H.: Nature 440, 58 (2006)

    Article  ADS  Google Scholar 

  8. Meier D.L., Koide S., Uchida Y.: Science 291, 84 (2001)

    Article  ADS  Google Scholar 

  9. Ustyugova G.V. et al.: ApJ 516, 221 (1999)

    Article  ADS  Google Scholar 

  10. Krasnopolsky R., Li Z.Y., Blandford R.D.: ApJ 595, 631 (2003)

    Article  ADS  Google Scholar 

  11. Aguilera D.N., Pons J.A., Miralles J.A.: ApJ 673, L167 (2008)

    Article  ADS  Google Scholar 

  12. Hennebelle P., Fromang S.: A&A 477, 9 (2008)

    Article  ADS  MATH  Google Scholar 

  13. Medin Z., Lai D.: MNRAS 382, 1833 (2007)

    ADS  Google Scholar 

  14. Li X.D., van den Heuvel E.P.J.: ApJ 513, L45 (1999)

    Article  ADS  Google Scholar 

  15. Pavlov G.G., Bezchastnov V.G.: ApJ 635, L61 (2005)

    Article  ADS  Google Scholar 

  16. Ibrahim A.I., Swank J.H., Parke W.: ApJ 584, L17 (2003)

    Article  ADS  Google Scholar 

  17. Schwarzschild K.: Sitzungsberichte der Kniglich Preussis- chen Akademie der Wissenschaften 1, 189 (1916)

    Google Scholar 

  18. Schwarzschild K.: Sitzungsberichte der Kniglich Preussis- chen Akademie der Wissenschaften 1, 424 (1916)

    Google Scholar 

  19. Kerr R.P.: Phys. Rev. Lett. 11, 237 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Newman E.T. et al.: J. Math. Phys. 6, 918 (1965)

    Article  ADS  Google Scholar 

  21. Reissner H.: Ann. Phys. Berlin 50, 106 (1916)

    Article  ADS  Google Scholar 

  22. Nordstr m G.: Verhandl. Koninkl. Ned. Akad. Weten-oschap. 20, 1231 (1918)

    ADS  Google Scholar 

  23. Polanco J., Letelier P., Ujevic M.: Phys. Rev. D 78, 024026 (2008)

    Article  ADS  Google Scholar 

  24. Bonnor W.A., Sackfield A.: Commun. Math. Phys. 8, 338 (1968)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Morgan L., Morgan T.: Phys. Rev. 183, 1097 (1969)

    Article  ADS  Google Scholar 

  26. Morgan L., Morgan T.: Phys. Rev. D 2, 2756 (1970)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. González G.A., Letelier P.S.: Class. Quantum Grav. 16, 479 (1999)

    Article  ADS  MATH  Google Scholar 

  28. Lynden-Bell D., Pineault S.: Mon. Not. R. Astron. Soc. 185, 679 (1978)

    ADS  MATH  Google Scholar 

  29. Chamorro A., Gregory R., Stewart J.M.: Proc R Soc Lond A 413, 251 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  30. Letelier P.S., Oliveira S.R.: J. Math. Phys. 28, 165 (1987)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Lemos J.P.S.: Class. Quantum Grav. 6, 1219 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Lemos J.P.S., Letelier P.S.: Class. Quantum Grav. 10, L75 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  33. Bic̆ák J., Lynden-Bell D., Katz J.: Phys. Rev. D 47, 4334 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  34. Bic̆ák J., Lynden-Bellm D., Pichon C.: Mon. Not. R. Astron. Soc. 265, 126 (1993)

    ADS  Google Scholar 

  35. González G.A., Espitia O.A.: Phys. Rev. D 68, 104028 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  36. Bic̆ák J., Ledvinka T.: Phys. Rev. Lett. 71, 1669 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  37. González G.A., Letelier P.S.: Phys. Rev. D 62, 064025 (2000)

    Article  ADS  Google Scholar 

  38. Ledvinka, T., Bic̆ák, J., Z̆ofka, M. In: Proceeding of 8th Marcel-Grossmann meeting in Gen. Relativ., edited by T. Piran (World Scientific, Singapore, 1999)

  39. García-Reyes G., González G.A.: Brazilian J. Phys. 37(3B), 1094 (2007)

    Article  ADS  Google Scholar 

  40. Letelier P.S.: Phys. Rev. D 60, 104042 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  41. Katz J., Bic̆ák J., Lynden-Bell D.: Class. Quantum Grav. 16, 4023 (1999)

    Article  ADS  MATH  Google Scholar 

  42. García G., González G.A.: Phys. Rev. D 69, 124002 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  43. Vogt D., Letelier P.S.: Phys. Rev. D 70, 064003 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  44. García-Reyes G., González G.A.: Class. Quantum Grav. 21, 4845 (2004)

    Article  ADS  MATH  Google Scholar 

  45. García-Reyes G., González G.A.: Phys. Rev. D 70, 104005 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  46. Synge J.L.: Relativity: The General Theory. North-Holland, Amsterdam (1966)

    Google Scholar 

  47. Neugebauer G., Meinel R.: Phys. Rev. Lett. 75, 3046 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. Klein C.: Class. Quantum Grav. 14, 2267 (1997)

    Article  ADS  MATH  Google Scholar 

  49. Klein C., Richter O.: Phys. Rev. Lett. 83, 2884 (1999)

    Article  ADS  Google Scholar 

  50. Klein C.: Phys. Rev. D 63, 064033 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  51. Frauendiener J., Klein C.: Phys. Rev. D 63, 084025 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  52. Klein C.: Phys. Rev. D 65, 084029 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  53. Klein C.: Phys. Rev. D 68, 027501 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  54. Klein C.: Ann. Phys. (Leipzig) 12, 599 (2003)

    Article  ADS  MATH  Google Scholar 

  55. Vokrouhlicky D., Karas V.: Astron. Astrophys. 243, 165 (1991)

    ADS  Google Scholar 

  56. Sengupta S.: Int. J. Mod. Phys. D 6, 591 (1997)

    Article  ADS  Google Scholar 

  57. de Felice F., Sorge F.: Class. Quantum Grav. 20, 469 (2003)

    Article  ADS  MATH  Google Scholar 

  58. Kovář J., Kopáček O., Karas V., Stuchlík Z.: Class. Quantum Grav. 27, 135006 (2010)

    Article  ADS  Google Scholar 

  59. Frank J., King A., Raine D.: Accretion Power in Astrophysics. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  60. Belvedere, G. In: Proceedings of Eur. Phys. Soc. Stud. Conf., Accretion disks and magnetic fields in astrophysics Kluwer, Dordrecht (1998)

  61. Aliev A.N., Ozdemir N.: Mon. Not. R. Astron. Soc. 336, 241 (2002)

    Article  ADS  Google Scholar 

  62. Braithwaite J., Spruit H.C.: Nature 431, 819 (2004)

    Article  ADS  Google Scholar 

  63. Rubin V.C., Graham J.A., Kenney J.D.P.: Ap. J. 394, L9 (1992)

    Article  ADS  Google Scholar 

  64. Rix H., Franx M., Fisher D., Illingworth G.: Ap. J. 400, L5 (1992)

    Article  ADS  Google Scholar 

  65. Bertola F. et al.: Ap. J. 458, L67 (1996)

    Article  ADS  Google Scholar 

  66. Struck C.: Phys. Rep. 321, 1 (1999)

    Article  ADS  Google Scholar 

  67. Ciri R., Bettoni D., Galletta G.: Nature 375, 661 (1995)

    Article  ADS  Google Scholar 

  68. Rayleigh Lord.: Proc. R. Soc. Lond. A 93, 148 (1917)

    Article  ADS  Google Scholar 

  69. Landau L.D., Lifshitz E.M.: Fluid Mechanics. Addison-Wesley, Reading, MA (1989)

    Google Scholar 

  70. Letelier P.S.: Phys. Rev. D 68, 104002 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  71. Ernst F.J.: Phys. Rev. 167, 1175 (1968)

    Article  ADS  Google Scholar 

  72. Ernst F.J.: Phys. Rev. 168, 1415 (1968)

    Article  ADS  Google Scholar 

  73. Kramer D., Stephani H., Herlt E., McCallum M.: Exact Solutions of Einsteins’s Field Equations. Cambridge University Press, Cambridge, England (1980)

    Google Scholar 

  74. Bonnor W.B.: Z. Phys. 190, 444 (1966)

    Article  MathSciNet  ADS  Google Scholar 

  75. Bateman, H.: Higher Transcendental Functions vol 2. McGraw Hill, New York

  76. Arfken, G.: Mathematical Methods for Physicists, Academic Press

  77. Scott S.M., Szekeres P.: Gen. Relativ. Gravit. 18, 557 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  78. Scott S.M., Szekeres P.: Gen. Relativ. Gravit. 18, 571 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  79. Bardeen J.M., Carter B., Hawking S.W.: Commun. Math. Phys. 31, 161 (1973)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  80. Quevedo H.: Phys. Rev. D 39(10), 2904 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  81. Chazy J.: Bull. Soc. Math. France 52, 17 (1924)

    MathSciNet  MATH  Google Scholar 

  82. Curzon H.E.J.: Proc. Lond. Math. Soc. 23, 477 (1924)

    Article  MATH  Google Scholar 

  83. Chandrasekhar S.: The Mathematical Theory of Black holes, pp. 623. Oxford Publications, New York (1992)

    Google Scholar 

  84. Zipoy D.M.: J. Math. Phys. 7, 1137 (1966)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  85. Voorhees B.H.: Phys. Rev. D 2, 2119 (1970)

    Article  ADS  Google Scholar 

  86. Schwarzschild, K.: Sitzungsber. Preuss. Akad. Wiss., 189 (1916)

  87. Erez G., Rosen N.: Bull. Res. Counc. Isr. 8, 47 (1959)

    MathSciNet  Google Scholar 

  88. González G.A., Ramos J.F.: Rev. Col. Fís. 33(2), 118 (2001)

    Google Scholar 

  89. Papapetrou A., Hamouni A.: Ann. Inst. Henri Poincaré 9, 179 (1968)

    ADS  Google Scholar 

  90. Lichnerowicz A.C.R.: Acad. Sci. 273, 528 (1971)

    MathSciNet  MATH  Google Scholar 

  91. Taub A.H.: J. Math. Phys. 21, 1423 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  92. Israel E.: Nuovo Cimento 44B, 1 (1966)

    ADS  Google Scholar 

  93. Israel E.: Nuovo Cimento 48B, 463 (1967)

    ADS  Google Scholar 

  94. Kuzmin G.G.: Astron. Zh. 33, 27 (1956)

    Google Scholar 

  95. Toomre A.: Ap. J. 138, 385 (1962)

    Article  MathSciNet  ADS  Google Scholar 

Download references

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  1. Departamento de Física, Universidad Tecnológica de Pereira, A. A. 97, Pereira, Colombia

    Cristian H. García-Duque & Gonzalo García-Reyes

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  1. Cristian H. García-Duque
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  2. Gonzalo García-Reyes
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Correspondence to Gonzalo García-Reyes.

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García-Duque, C.H., García-Reyes, G. General magnetized Weyl solutions: disks and motion of charged particles. Gen Relativ Gravit 43, 3001–3032 (2011). https://doi.org/10.1007/s10714-011-1219-1

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