Abstract
In continuation of recent work done by the present authors (Int. J. Theor. Phys. 2013, doi:10.1007/s10773-013-1538-y, hereafter paper I) some new exact families of static spherically symmetric perfect fluid solution of Einstein–Maxwell gravitational field equations are presented. These solutions and the corresponding equations of state, presented in parametric form, may be astrophysically significant in constructing relativistic stellar models of electrically charged self-bound stars.
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Fatema, S., Murad, H.M.: An exact family of Einstein–Maxwell Wyman–Adler solution in general relativity. Int. J. Theor. Phys. (2013). doi:10.1007/s10773-013-1538-y
Patel, L.K., Pandya, B.M.: A Reissner–Nordström interior solution. Acta Phys. Hung., Heavy Ion Phys. 60, 57–65 (1986). doi:10.1007/BF03157418
Patel, L.K., Koppar, S.S.: A charged analogue of the Vaidya–Tikekar solution. Aust. J. Phys. 40, 441–447 (1987). doi:10.1071/PH870441
Koppar, S.S., Patel, L.K., Singh, T.: On relativistic charged fluid spheres. Acta Phys. Hung., Heavy Ion Phys. 69, 53–62 (1991). doi:10.1007/BF03054133
Patel, L.K., Tikekar, R., Sabu, M.C.: Exact interior solutions for charged fluid spheres. Gen. Relativ. Gravit. 29, 489–497 (1997). doi:10.1023/A:1018886816863
Sharma, R., Mukherjee, S., Maharaj, S.D.: General solution for a class of static charged spheres. Gen. Relativ. Gravit. 33, 999–1009 (2001). doi:10.1023/A:1010272130226
Komathiraj, K., Maharaj, S.D.: Tikekar superdense stars in electric fields. J. Math. Phys. 48, 042501 (2007). doi:10.1063/1.2716204
Lattimer, J.M., Prakash, M.: Neutron star structure and the equation of state. Astrophys. J. 550, 426–442 (2001). doi:10.1086/319702
Lattimer, J.M.: The structure of strange quark matter and neutron stars. J. Phys. G, Nucl. Part. Phys. 30, S479–S486 (2004). doi:10.1088/0954-3899/30/1/056
Lattimer, J.M., Prakash, M.: Ultimate energy density of observable cold baryonic matter. Phys. Rev. Lett. 94, 111101 (2005). doi:10.1103/PhysRevLett.94.111101
Delgaty, M.S.R., Lake, K.: Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein’s equations. Comput. Phys. Commun. 115, 395–415 (1998). doi:10.1016/S0010-4655(98)00130-1
Negreiros, R.P., Weber, F., Malheiro, M., Vladimir, U.: Electrically charged strange quark stars. Phys. Rev. D 80, 083006 (2009). doi:10.1103/PhysRevD.80.083006
Komathiraj, K., Maharaj, S.D.: Analytical models of quark stars. Int. J. Mod. Phys. D 16, 1803–1811 (2011). doi:10.1142/S0218271807011103
Mak, M.K., Harko, T.: Quark stars admitting a one-parameter group of conformal motions. Int. J. Mod. Phys. D 13, 149–156 (2004). doi:10.1142/S0218271804004451
Rahaman, F., Sharma, R., Ray, S., Maulick, R., Karar, I.: Strange stars in Krori–Barua space-time. Eur. Phys. J. C 72, 2071 (2012). doi:10.1140/epjc/s10052-012-2071-5
Sharma, R., Karmakar, S., Mukherjee, S.: Maximum mass of a class of cold compact stars. Int. J. Mod. Phys. D 15, 405–418 (2006). doi:10.1142/S0218271806008012
Tikekar, R., Jotania, K.: On relativistic models of strange stars. Pramana J. Phys. 68, 397–406 (2007)
Chattopadhyay, P.K., Deb, R., Paul, B.C.: Relativistic solution for a class of static compact charged star in pseudo-spheroidal spacetime. Int. J. Mod. Phys. D 21, 1250071 (2012). doi:10.1142/S021827181250071X
Kalam, M., Usmani, A., Rahaman, F., Hossein, S.M., Karar, I., Sharma, R.: A relativistic model for strange quark stars. Int. J. Theor. Phys. (2012). doi:10.1007/s10773-013-1629-9
Durgapal, M.C.: A class of new exact solutions in general relativity. J. Phys. A, Math. Gen. 15, 2637–2644 (1982). doi:10.1088/0305-4470/15/8/039
Mak, M.K., Fung, P.C.W.: Charged static fluid spheres in general relativity. Nuovo Cimento B 110, 897–903 (1995). doi:10.1007/BF02722858
Mak, M.K., Fung, P.C.W., Harko, T.: New classes of interior solutions to Einstein–Maxwell equations in spherical symmetry. Nuovo Cimento B 111, 1461–1464 (1996). doi:10.1007/BF02741485
Ishak, M., Chamandy, L., Neary, N., Lake, K.: Exact solutions with w modes. Phys. Rev. D 64, 024005 (2001). doi:10.1103/PhysRevD.64.024005
Lake, K.: All static spherically symmetric perfect-fluid solutions of Einstein’s equations. Phys. Rev. D 67, 104015 (2003). doi:10.1103/PhysRevD.67.104015
Maurya, S.K., Gupta, Y.K.: On a family of well behaved perfect fluid balls as astrophysical objects in general relativity. Astrophys. Space Sci. 334, 145–154 (2011). doi:10.1007/s10509-011-0705-y
Tolman, R.C.: Static solutions of Einstein’s field equations for spheres of fluid. Phys. Rev. 55, 364–373 (1939). doi:10.1103/PhysRev.55.364
Pant, N., Rajasekhara, S.: Variety of well behaved parametric classes of relativistic charged fluid spheres in general relativity. Astrophys. Space Sci. 333, 161–168 (2011). doi:10.1007/s10509-011-0607-z
Pant, N., Negi, P.S.: Variety of well behaved exact solutions of Einstein–Maxwell field equations strange quark stars, neutron stars and pulsars. Astrophys. Space Sci. 338, 163–169 (2012). doi:10.1007/s10509-011-0919-z
Wyman, M.: Radially symmetric distribution of matter. Phys. Rev. 75, 1930–1936 (1949). doi:10.1103/PhysRev.75.1930
Adler, R.J.: A fluid sphere in general relativity. J. Math. Phys. 15, 727–729 (1974). doi:10.1063/1.1666717
Adams, R.C., Warburton, R.D., Cohen, J.M.: Analytic stellar models in general relativity. Astrophys. J. 200, 263–268 (1975). doi:10.1086/153627
Kuchowicz, B.: A physically realistic sphere of perfect fluid to serve as a model of neutron stars. Astrophys. Space Sci. 33, L13–L14 (1975). doi:10.1007/BF00646028
Pant, M.J., Tewari, B.C.: Well behaved class of charge analogue of Adler’s relativistic exact solution. J. Mod. Phys. 2, 481–487 (2011). doi:10.4236/jmp.2011.26058
Pant, N., Tewari, B.C., Fuloria, P.: Well behaved parametric class of exact solutions of Einstein–Maxwell field equations in general relativity. J. Mod. Phys. 2, 1538–1543 (2011). doi:10.4236/jmp.2011.212186
Pant, N., Faruqi, S.: Relativistic modeling of a superdense star containing a charged perfect fluid. Gravit. Cosmol. 18, 204–210 (2012). doi:10.1134/S0202289312030073
Murad, H.M.: A new well behaved class of charge analogue of Adler’s relativistic exact solution. Astrophys. Space Sci. 343, 187–194 (2013). doi:10.1007/s10509-012-1258-4
Heintzmann, H.: New exact static solutions of Einsteins field equations. Z. Phys. 228, 489–493 (1969). doi:10.1007/BF01558346
Korkina, M.P.: Static configuration with an ultrarelativistic equation of state at the center. Sov. Phys. J. 24, 468–470 (1981). doi:10.1007/BF00898413
Pant, N., Mehta, R.N., Pant, M.J.: Well behaved class of charge analogue of Heintzmann’s relativistic exact solution. Astrophys. Space Sci. 332, 473–479 (2011). doi:10.1007/s10509-010-0509-5
Pant, N., Maurya, S.K.: Relativistic modeling of charged super-dense star with Einstein–Maxwell equations in general relativity. Appl. Math. Comput. 218, 8260–8268 (2012). doi:10.1016/j.amc.2012.01.044
Pant, N.: Well behaved parametric class of relativistic charged fluid ball in general relativity. Astrophys. Space Sci. 332, 403–408 (2011). doi:10.1007/s10509-010-0521-9
Mehta, R.N., Pant, N., Mahto, D., Jha, J.S.: A well-behaved class of charged analogue of Durgapal solution. Astrophys. Space Sci. 343, 653–660 (2013). doi:10.1007/s10509-012-1289-x
Murad, H.M., Fatema, S.: A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity. Astrophys. Space Sci. 343, 587–597 (2013). doi:10.1007/s10509-012-1277-1
Maurya, S.K., Gupta, Y.K., Pratibha: Regular and well-behaved relativistic charged superdense star models. Int. J. Mod. Phys. D 20, 1289–1300 (2011). doi:10.1142/S0218271811019414
Faruqi, S., Pant, N.: Well-behaved relativistic charged super-dense star models. Astrophys. Space Sci. 341, 485–490 (2012). doi:10.1007/s10509-012-1132-4
Orlyansky, O.Y.: Singularity-free static fluid spheres in general relativity. J. Math. Phys. 38, 5301–5304 (1997). doi:10.1063/1.531943
Gupta, Y.K., Maurya, S.K.: A class of regular and well behaved relativistic super-dense star models. Astrophys. Space Sci. 332, 155–162 (2011). doi:10.1007/s10509-010-0503-y
Fuloria, P., Tewari, B.C., Joshi, B.C.: Well behaved class of charge analogue of Durgapal’s relativistic exact solution. J. Mod. Phys. 2, 1156–1160 (2011). doi:10.4236/jmp.2011.210143
Fuloria, P., Tewari, B.C.: A family of charge analogue of Durgapal solution. Astrophys. Space Sci. 341, 469–475 (2012). doi:10.1007/s10509-012-1105-7
Murad, H.M., Fatema, S.: A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity II. Astrophys. Space Sci. 344, 69–78 (2013). doi:10.1007/s10509-012-1320-2
Pant, N.: Some new exact solutions with finite central parameters and uniform radial motion of sound. Astrophys. Space Sci. 331, 633–644 (2011). doi:10.1007/s10509-010-0453-4
Maurya, S.K., Gupta, Y.K.: A family of well behaved charge analogues of a well behaved neutral solution in general relativity. Astrophys. Space Sci. 332, 481–490 (2011). doi:10.1007/s10509-010-0541-5
Pant, N.: New class of well behaved exact solutions of relativistic charged white-dwarf star with perfect fluid. Astrophys. Space Sci. 334, 267–271 (2011). doi:10.1007/s10509-011-0720-z
Pant, N.: New class of well behaved exact solutions for static charged neutron-star with perfect fluid. Astrophys. Space Sci. 337, 147–150 (2012). doi:10.1007/s10509-011-0809-4
Maurya, S.K., Gupta, Y.K., Pratibha: A class of charged relativistic superdense star models. Int. J. Theor. Phys. 51, 943–953 (2012). doi:10.1007/s10773-011-0968-7
Maurya, S.K., Gupta, Y.K.: Extremization of mass of charged superdense star models describe by Durgapal type space-time metric. Astrophys. Space Sci. 334, 301–310 (2011). doi:10.1007/s10509-011-0736-4
Maurya, S.K., Gupta, Y.K.: A new family of polynomial solutions for charged fluid spheres. Nonlinear Anal., Real World Appl. 13, 677–685 (2012). doi:10.1016/j.nonrwa.2011.08.008
Kuchowicz, B.: Differential conditions for physically meaningful fluid spheres in general relativity. Phys. Lett. A 38, 369–370 (1972). doi:10.1016/0375-9601(72)90164-8
Buchdahl, H.A.: Regular general relativistic charged fluid spheres. Acta Phys. Pol. B 10, 673–685 (1979)
Böhmer, C.G., Harko, T.: Minimum mass radius ratio for charged gravitational objects. Gen. Relativ. Gravit. 39, 757–775 (2007). doi:10.1007/s10714-007-0417-3
Andréasson, H.: Sharp bounds on the critical stability radius for relativistic charged spheres. Commun. Math. Phys. 288, 715–730 (2009). doi:10.1007/s00220-008-0690-3
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Authors acknowledge their sincere gratitude to the reviewers for pointing out the errors and making relevant constructive suggestions that help authors improve the original manuscript.
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This work is respectfully dedicated to the memory of our esteemed Professor J.N. Islam (1939–2013). With his death, we have lost a creative, thoughtful and an active member of the relativity-and-gravitation community.
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Murad, M.H., Fatema, S. Some Exact Relativistic Models of Electrically Charged Self-bound Stars. Int J Theor Phys 52, 4342–4359 (2013). https://doi.org/10.1007/s10773-013-1752-7
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DOI: https://doi.org/10.1007/s10773-013-1752-7