New classes of exact solutions in relativistic astrophysics.
Matondo, Didier Kileba.
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The description of highly compact objects in a general relativistic setting is a problem of present research. The relativistic e ects arising from the presence of the electric eld and anisotropy are included in our model. We nd new exact solutions to the Einstein- Maxwell eld equations which are relevant in the description of highly compact stellar objects. Firstly we adopt the approach used by Mafa Takisa and Maharaj (2013b) to obtain a new class of solutions for a di erent form of the electric eld intensity. Our models contain a linear equation of state that is consistent with a quark star. It is interesting that we regain the quark models of Thirukkanesh and Maharaj (2008). Secondly we generalise the charged model of Hansraj and Maharaj (2006) by adding anisotropy to the eld equations. Several new classes of exact solutions are found to the Einstein-Maxwell system in terms of Bessel functions and elementary functions. Our solutions contain the neutron star model of Finch and Skea (1989). A physical analysis indicates that the matter distributions are well behaved and regular throughout the stellar structure. Therefore the models found may be useful in modelling a charged anisotropic compact sphere.