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Some charged polytropic models. (English) Zbl 1277.83032

Summary: The Einstein-Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of T. Feroze and A. A. Siddiqui [Gen. Relativ. Gravitation 43, No. 4, 1025–1035 (2011; Zbl 1216.83031)] and the authors [Gen. Relativ. Gravitation 44, No. 6, 1419–1432 (2012; Zbl 1243.83025)] are recovered. We also obtain exact solutions for a neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the energy density, tangential pressure and anisotropy profiles are consistent with earlier treatments which suggest relevance in describing relativistic compact stars.

MSC:

83C22 Einstein-Maxwell equations
83C15 Exact solutions to problems in general relativity and gravitational theory
78A25 Electromagnetic theory (general)
85A15 Galactic and stellar structure
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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