Browsing by Author "Takisa, Pedro Mafa."

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Exact models of compact stars with equations of state.
(2013) Takisa, Pedro Mafa.; Maharaj, Sunil Dutt.
We study exact solutions to the Einstein-Maxwell system of equations and relate them to compact objects. It is well known that there are substantial analytic difficulties in the modelling of self-gravitating, static fluid spheres when the pressure explicitly depends on the matter density. Much simplification in solving the Einstein-Maxwell equations is achieved with the introduction of electric charge and anisotropic matter. In this thesis, in order to obtain analytical solutions, we consider the general situation of anisotropy in the presence of electric charge satisfying a barotropic equation of state. Firstly, a linear equation of state, secondly a quadratic equation of state, and thirdly a polytropic equation of state are analysed. For each of these equations of state the Einstein-Maxwell equations are integrated and exact solutions are found in terms of elementary functions. By choosing specific rational forms for one of the gravitational potential and particular forms for the electric charge, new classes of solutions in static spherically symmetric interior spacetimes are generated in the presence of electric charge. It is interesting to note that, from our new class of solutions with an equation of state, we can regain earlier models. A detailed physical analysis performed indicates that the classes of solutions are physically reasonable. We regain the current accurate observed masses for the binary pulsars PSR J1614-2230 , PSR J1903+327, Vela X-1, SMC X-1 and Cen X-3.
New realistic solutions for charged matter with an equation of state.
Takisa, Pedro Mafa.; Maharaj, Sunil Dutt.
The purpose of this thesis is to provide new exact solutions to the Einstein-Maxwell system which are physically reasonable. We assume that the spacetime is static and spherically symmetric with a charged anisotropic matter distribution. The equation of state is linear. We show that the class of models found by Thirukkanesh and Maharaj (2008) has a singularity in the charge density at the centre of the sphere. Two new exact classes of solutions to the Einstein-Maxwell are found in terms of elementary functions. This contains models in which there is no singularity in charge density. From our general models, we can regain the Thirukkanesh and Maharaj (2008) models and other models as special cases. The physical analysis show that the solutions are relevant for the description of realistic compact relativistic stars. We demonstrate that the mass corresponds to a compact relativistic body with anisotropy in presence of charge. We show that the electromagnetic field appreciably affects the value of the mass. A detailed physical analysis of the matter variables and electromagnetic quantities is performed. The models generated are consistent with the quark stars containing strange matter.