New families of exact solutions for compact stars.
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Date
2018
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Abstract
In this thesis we present new families of exact solutions to the Einstein and Einstein-
Maxwell eld equations which are relevant in the description of highly compact stellar
objects. We rst impose a linear equation of state to generate exact solutions in
terms of elementary functions which contain earlier quark models, including those
of Thirukkanesh and Maharaj (Class. Quantum Grav. 25, 235001 (2008)) and
Mafa Takisa and Maharaj (Astrophys. Space Sci. 354, 463 (2013)). Secondly, we
nd exact solutions in terms of elementary functions, Bessel and modi ed Bessel
functions through the Finch and Skea geometry which satisfy all criteria for physical
acceptability. From these models we regain the uncharged model of Finch and Skea
(Class. Quantum Grav. 6, 467 (1989)) and the charged model of Hansraj and
Maharaj (Int. J. Mod. Phys. D 15, 1311 (2006)) as particular cases. Thirdly, we nd
new exact stellar models by imposing a symmetry condition on spacetime, namely
a conformal Killing vector. We nd solutions to the eld equations with the help of
the gravitational potentials related explicitly by the conformal vector established by
Manjonjo et al (Eur. Phys. J. Plus 132, 62 (2017)). For each approach, we select
a particular model to study the physical features and then masses and radii with
accurate ranges consistent with observed numerical values of compact objects such
as SAX J1808.4-3658, LMC X-4, SMC X-1, EXO 1785, Cen X-3, 4U1820-30, PSR
J1903+327, Vela X-1 and PSR J1614-2230 are generated. The physical features in
all cases are studied comprehensively, and we show that our solutions are stable, well
behaved and have realistic physical features.
Description
Doctoral degree. University of KwaZulu-Natal, Durban.