Browsing by Author "Moopanar, Selvandren."

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Conformal symmetries and classification in shear-free spherically symmetric spacetimes.
(2014) Manjonjo, Addial Mackingtosh.; Maharaj, Sunil Dutt.; Moopanar, Selvandren.
In this thesis we study the conformal geometry of static and non-static spherically symmetric spacetimes. We analyse the general solution of the conformal Killing vector equation subject to integrability conditions which place restrictions on the metric func- tions. TheWeyl tensor is used to characterise the conformal geometry, and we calculate the Weyl tensor components for the spherically symmetric line element. The accuracy of our results is veri ed using Mathematica (Wolfram 2010) and Maple (2009). We show that the standard result in the conformal motions for static spacetimes is in- correct. This mistake is identi ed and corrected. Two nonlinear ordinary differential equations are derived in the classi cation of static spacetimes. Both equations are solved in general. Two nonlinear partial differential equations are derived in the classi- cation of non-static spacetimes. The rst equation is solved in general and the second equation admits a particular solution. Our treatment is the rst complete classi cation of conformal motions in static and non-static spherically symmetric spacetimes using the Weyl tensor.
Conformal symmetry and applications to spherically symmetric spacetimes.
(2018) Manjonjo, Addial Mackingtosh.; Maharaj, Sunil Dutt.; Moopanar, Selvandren.
In this thesis we study static spherically symmetric spacetimes with a spherical conformal symmetry and a nonstatic conformal factor. We analyse the general solution of the conformal Killing vector equation subject to integrability conditions which impose restrictions on the metric functions. The Weyl tensor is used to characterise the conformal geometry. An explicit relationship between the gravitational potentials for both conformally and nonconformally at cases is obtained. The Einstein equations can then be written in terms of a single gravitational potential. Previous results of conformally invariant static spheres are special cases of our solutions. For isotropic pressure we can find all metrics explicitly and show that the models always admit a barotropic equation of state. We show that this treatment contains well known metrics such Schwarzschild (interior), Tolman, Kuchowicz, Korkina and Orlyanskii, Patwardhan and Vaidya, and Buchdahl and Land. For anisotropic pressures the solution of the fluid equations is found in general. We then consider an astrophysical application of conformal symmetries. We investigate spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. We generate a new anisotropic solution to the Einstein field equations. We demonstrate that this exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass-radius limit and the surface red shift are consistent with observational constraints.
On Stephani universes.
(1992) Moopanar, Selvandren.; Maharaj, Sunil Dutt.
In this dissertation we study conformal symmetries in the Stephani universe which is a generalisation of the Robertson-Walker models. The kinematics and dynamics of the Stephani universe are discussed. The conformal Killing vector equation for the Stephani metric is integrated to obtain the general solution subject to integrability conditions that restrict the metric functions. Explicit forms are obtained for the conformal Killing vector as well as the conformal factor . There are three categories of solution. The solution may be categorized in terms of the metric functions k and R. As the case kR - kR = 0 is the most complicated, we provide all the details of the integration procedure. We write the solution in compact vector notation. As the case k = 0 is simple, we only state the solution without any details. In this case we exhibit a conformal Killing vector normal to hypersurfaces t = constant which is an analogue of a vector in the k = 0 Robertson-Walker spacetimes. The above two cases contain the conformal Killing vectors of Robertson-Walker spacetimes. For the last case in - kR = 0, k =I 0 we provide an outline of the integration process. This case gives conformal Killing vectors which do not reduce to those of RobertsonWalker spacetimes. A number of the calculations performed in finding the solution of the conformal Killing vector equation are extremely difficult to analyse by hand. We therefore utilise the symbolic manipulation capabilities of Mathematica (Ver 2.0) (Wolfram 1991) to assist with calculations.