Dissipative cylindrical collapse of charged anisotropic fluid. (English) Zbl 1298.83081
Summary: We have studied the dynamics of a cylindrical column of anisotropic, charged fluid which is experiencing dissipation in the form of heat flow, free-streaming radiation, and shearing viscosity, undergoing gravitational collapse. We calculate the Einstein-Maxwell field equations and, using the Darmois junction conditions, match the interior non-static cylindrically symmetric space-time with the exterior anisotropic, charged, cylindrically symmetric space-time. The behavior of the density, pressure and luminosity of the collapsing matter has been analyzed. From the dynamical equations, the effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we have derived the solutions for the collapsing matter which is valid during the later stages of collapse and have discussed the significance from a physical standpoint.
MSC:
| 83C57 | Black holes |
Keywords:
gravitational collapse; cylindrical symmetry; electromagnetic field; dissipation; junction conditions; dynamical equations; solutionsReferences:
| [1] | Joshi, PS; Malafarina, D., No article title, Int. J. Mod. Phys. D, 20, 2641 (2011) · Zbl 1263.83011 · doi:10.1142/S0218271811020792 |
| [2] | Singh, TP, No article title, J. Astrophys. Astr., 20, 221 (1999) · doi:10.1007/BF02702354 |
| [3] | Milne, EA, No article title, Mon. Not. R. Astr. Soc, 91, 4 (1930) |
| [4] | Chandrasekhar, S., No article title, Mon. Not. R. Astr. Soc., 91, 456 (1931) · Zbl 0002.10101 |
| [5] | Chandrasekhar, S.: ibid 95, 207 (1935) |
| [6] | Chandrasekhar, S., No article title, Astrophys. J., 74, 81 (1931) · Zbl 0002.23502 · doi:10.1086/143324 |
| [7] | Chandrasekhar, S.: Observatory 57, 373 (1934) |
| [8] | Zwicky, F., No article title, Astrophys. J., 88, 522 (1938) · doi:10.1086/144003 |
| [9] | Openheimer, JR; Snyder, H., No article title, Phys. Rev., 56, 455 (1939) · Zbl 0022.28104 · doi:10.1103/PhysRev.56.455 |
| [10] | Vaidya, PC, No article title, Curr. Sci., 12, 183 (1943) |
| [11] | Vaidya, PC, No article title, Proc. Indian Acad. Sci. A, 33, 264 (1951) · Zbl 0044.42202 |
| [12] | Vaidya, PC, No article title, Phys. Rev., 83, 10 (1951) · Zbl 0044.23002 · doi:10.1103/PhysRev.83.10 |
| [13] | Vaidya, PC, No article title, Nature, 171, 260 (1953) · Zbl 0050.21304 · doi:10.1038/171260a0 |
| [14] | Misner, CW; Sharp, D., No article title, Phys. Rev. B, 136, 571 (1964) · doi:10.1103/PhysRev.136.B571 |
| [15] | Misner, CW, No article title, Phys. Rev. B, 137, 1360 (1965) · doi:10.1103/PhysRev.137.B1360 |
| [16] | Lindquist, RW; Schwartz, RA; Misner, CW, No article title, Phys. Rev. B, 137, 1364 (1965) · doi:10.1103/PhysRev.137.B1364 |
| [17] | Lake, K.; Hellaby, C., No article title, Phys. Rev. D, 24, 3019 (1981) · Zbl 1267.83122 · doi:10.1103/PhysRevD.24.3019 |
| [18] | Santos, NO, No article title, Mon. Not. R. Astr. Soc., 216, 403 (1985) |
| [19] | Herrera, L.; Santos, NO, No article title, Phys. Rep., 286, 53 (1997) · doi:10.1016/S0370-1573(96)00042-7 |
| [20] | Herrera, L.; Prisco, A.; Hernandez-Pastora, JL; Santos, NO, No article title, Phys. Lett. A, 237, 113 (1998) · doi:10.1016/S0375-9601(97)00874-8 |
| [21] | Herrera, L.; Le Denmat, G.; Santos, NO, No article title, Phys. Rev. D, 79, 087505 (2009) · doi:10.1103/PhysRevD.79.087505 |
| [22] | Chan, R., No article title, Mon. Not. R. Astron. Soc., 316, 588 (2000) · doi:10.1046/j.1365-8711.2000.03547.x |
| [23] | Bonnor, WB; Oliveira, AKG; Santos, NO, No article title, Phys. Rep, 181, 269 (1989) · doi:10.1016/0370-1573(89)90069-0 |
| [24] | Banerjee, A.; Dutta Choudhury, SB; Bhui, BK, No article title, Phys. Rev. D, 40, 670 (1989) · doi:10.1103/PhysRevD.40.670 |
| [25] | Prisco, A.; Herrera, L.; Le Denmat, G.; MacCallum, MAH; Santos, NO, No article title, Phys. Rev. D, 76, 064017 (2007) · doi:10.1103/PhysRevD.76.064017 |
| [26] | Rosseland, S., No article title, Mon. Not. R. Astron. Soc., 84, 720 (1924) |
| [27] | Eddington, A.S.: Internal Constitution of the Stars. Cambridge University Press, Cambridge (1926) · JFM 52.1021.05 |
| [28] | Raychaudhuri, AK; De, UK, No article title, J. Phys. A, 3, 263 (1970) · doi:10.1088/0305-4470/3/3/011 |
| [29] | Olson, E.; Bailyn, M., No article title, Phys. Rev. D, 13, 2204 (1976) · doi:10.1103/PhysRevD.13.2204 |
| [30] | Bally, J.; Harrison, ER, No article title, Astrophys. J., 220, 743 (1978) · doi:10.1086/155961 |
| [31] | De Oliveira, A.K.G., Santtos, N.O.: Astrophys. Astrophys. J. 312, 640 (1987) |
| [32] | Usov, V., No article title, Phys. Rev. D, 70, 067301 (2004) · doi:10.1103/PhysRevD.70.067301 |
| [33] | Mak, M.; Harko, T., No article title, Int. J. Mod. Phys. D, 13, 149 (2004) · Zbl 1079.83513 · doi:10.1142/S0218271804004451 |
| [34] | Glass, EN, No article title, Phys. Lett., 86A, 351 (1981) · doi:10.1016/0375-9601(81)90553-3 |
| [35] | Herrera, L.; Prisco, A.; Martin, J.; Ospino, J.; Santos, NO; Troconis, O., No article title, Phys. Rev. D, 69, 084026 (2004) · doi:10.1103/PhysRevD.69.084026 |
| [36] | Mitra, A., No article title, Phys. Rev. D, 74, 024010 (2006) · doi:10.1103/PhysRevD.74.024010 |
| [37] | Sharma, R.; Tikekar, R., No article title, Gen. Relativ. Gravit., 44, 2503 (2012) · Zbl 1255.83091 · doi:10.1007/s10714-012-1406-8 |
| [38] | Shapiro, SL; Teukolsky, SA, No article title, Phys. Rev. Lett., 66, 994 (1991) · Zbl 0968.83515 · doi:10.1103/PhysRevLett.66.994 |
| [39] | Shapiro, SL; Teukolsky, SA, No article title, Phys. Rev. D, 45, 2006 (1992) · doi:10.1103/PhysRevD.45.2006 |
| [40] | Penrose, R.: Rivista del Nuovo Cimento. Numero Speziale I, 257 (1969) |
| [41] | Thorne, K.S.: In Magic without Magic : John Archibald Wheeler. In: Klauder (ed.) Freeman, San Francisco |
| [42] | Rosen, N.: Jubillee of relativity theory. In: Mercier, A., Kervaire, M. (eds.) Birkhauser Verlag, Basel (1956) |
| [43] | Einstein, A.; Rosen, N., No article title, J. Franklin Inst, 223, 43 (1937) · Zbl 0017.09601 · doi:10.1016/S0016-0032(37)90583-0 |
| [44] | Rosen, N., No article title, Bull. Res. Coun. Israel, 3, 528 (1953) |
| [45] | Thorne, KS, No article title, Phys. Rev. B, 138, 251 (1965) · doi:10.1103/PhysRev.138.B251 |
| [46] | Melvin, MA, No article title, Phys. Rev. B, 139, 225 (1965) · doi:10.1103/PhysRev.139.B225 |
| [47] | Melvin, MA, No article title, Phys. Lett., 8, 65 (1964) · Zbl 0118.23203 · doi:10.1016/0031-9163(64)90801-7 |
| [48] | Chiba, T., No article title, Prog. Theor. Phys., 95, 321 (1996) · doi:10.1143/PTP.95.321 |
| [49] | Nolan, BC, No article title, Phys. Rev. D, 65, 104006 (2002) · doi:10.1103/PhysRevD.65.104006 |
| [50] | Goncalves, SMCV; Jhingan, S., No article title, Int. J. Mod. Phys. D, 11, 1469 (2002) · Zbl 1062.83522 · doi:10.1142/S0218271802002128 |
| [51] | Pereira, PRCT; Wang, A., No article title, Phys. Rev. D, 62, 124001 (2000) · doi:10.1103/PhysRevD.62.124001 |
| [52] | Pereira, P.R.C.T., Wang, A.: Erratum-ibid. D 67, 129902 (2003) |
| [53] | Pereira, PRCT; Wang, A., No article title, Gen. Relativ. Gravit., 32, 2189 (2000) · Zbl 0968.83028 · doi:10.1023/A:1001954604324 |
| [54] | Hayward, SA, No article title, Class. Quantum Grav., 17, 1749 (2000) · Zbl 0983.83044 · doi:10.1088/0264-9381/17/8/302 |
| [55] | Goncalves, SMCV, No article title, Class. Quantum Grav., 20, 37 (2003) · Zbl 1024.83007 · doi:10.1088/0264-9381/20/1/303 |
| [56] | Prisco, A.; Herrera, L.; MacCallum, MAH; Santos, NO, No article title, Phys. Rev. D, 80, 064031 (2009) · doi:10.1103/PhysRevD.80.064031 |
| [57] | Sharif, M.; Abbas, G., No article title, Astrophys. Space Sci., 335, 515 (2011) · Zbl 1230.83069 · doi:10.1007/s10509-011-0761-3 |
| [58] | Sharif, M.; Fatima, S., No article title, Gen. Relativ. Gravit., 43, 127 (2011) · Zbl 1208.83082 · doi:10.1007/s10714-010-1076-3 |
| [59] | Here we follow the definition given by Hayward. See, Hayward, S. A.: Class. Quantum Grav. 17, 1749 (2000) |
| [60] | Poisson, E.: An Advanced Course in General Relativity. Lecture Notes, Deparment of Physics, University of Guelph (2002) |
| [61] | Poisson, E.: A Relativist’s Toolkit. Cambridge University Press (2004) · Zbl 1058.83002 |
| [62] | Chao-Guang, H., No article title, Acta. Phys. Sin. (overseas edition), 4, 617 (1995) · doi:10.1088/1004-423X/4/8/008 |
| [63] | Darmois, G.: Memorial des Sciences Mathematiques. Gautheir-Villars, Paris (1927). Fasc. 25 · JFM 53.0816.03 |
| [64] | Darmois, G.; Israel, W., No article title, Nuovo Cimento B, 44, 1 (1966) |
| [65] | Darmois, G.; Israel, W., No article title, ibid, 48, 463 (1966) |
| [66] | Eisenhart, L.P.: Riemannian geometry. Princeton University Press (1949) · Zbl 0041.29403 |
| [67] | Oliveira, AKG; Santtos, NO; Kolassis, CA, No article title, Mon. Not. R. Astron. Soc., 216, 1001 (1985) · Zbl 0572.76129 |
| [68] | Ghosh, SG; Deshkar, DW, No article title, Int. J. Mod. Phys. D, 12, 317 (2003) · doi:10.1142/S0218271803002433 |
| [69] | Nath, S.; Debnath, U.; Chakraborty, S., No article title, Astrophys. Space Sci., 313, 431 (2008) · Zbl 1194.83062 · doi:10.1007/s10509-007-9713-3 |
| [70] | Sharif, M.; Abbas, G., No article title, J. Phys. Soc. Japan, 80, 104002 (2011) · doi:10.1143/JPSJ.80.104002 |
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