Maharaj, Sunil Dutt.Ray, Subharthi.Kileba Matondo, Didier.2023-09-202023-09-2020182018https://researchspace.ukzn.ac.za/handle/10413/22286Doctoral degree. University of KwaZulu-Natal, Durban.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.enlinear equation.quark models.elementary functions.Thesis