New classes of exact solutions in relativistic astrophysics.
Date
2015
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Abstract
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.
Description
Master of Science in Mathematical, Statistics and Computer Sciences. University of KwaZulu-Natal, Durban 2015.
Keywords
Theses - Applied Mathematics.