Browsing by Author "Govender, Gabriel."

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Inhomogeneous solutions to the Einstein equations.
(2007) Govender, Gabriel.; Maharaj, Sunil Dutt.
In this dissertation we consider spherically symmetric gravitational fields that arise in relativistic astrophysics and cosmology. We first present a general review of static spherically symmetric spacetimes. aand highlight a particular class of exact solutions of the Einstein-Maxwell system for charged spheres. In the case of shear-free spacetimes with heat flow, the integration of the system is reduced to solving the condition of pressure isotropy. This condition is a second order linear differential equation with variable coefficients. By choosing particular forms for the gravitational potentials, sev-eral classes of new solutions are generated. We regain known solutions corresponding to coniformal flatness when tidal forces are absent. We also consider expanding, accelerating and shearing models when the heat flux is not present. A new general class of models is found. This new class of shearing solutions contains the model of Maharaj et al (1993) when a parameter is set to zero. Our new solution does not contain a singularity at the stellar centre, and it is therefore useful in modelling the interior of stars. Finally, we demonstrate that the shearing models obtained by Markund and Bradley (1999) do not satisfy the Einstein field equations.
Relativistic radiating stars with generalised atmospheres.
(2010) Govender, Gabriel.; Maharaj, Sunil Dutt.
In this dissertation we construct radiating models for dense compact stars in relativistic astrophysics. We first utilise the standard Santos (1985) junction condition to model Euclidean stars. By making use of the heuristic Euclidean condition and a linear transformation in the gravitational potentials, we generate a particular exact solution in closed form to the nonlinear stellar boundary condition. Earlier models of spherical nonadiabatic gravitational collapse are then extended by considering the effect of radial perturbations in the matter and metric variables, on the evolution of the stellar fluid and the dynamics of the collapse process. The governing equation describing the temporal behaviour of the model is solved on the stellar surface. The model becomes static in the later stages of collapse. The Santos junction condition is then generalised to describe a radiating star which has a two-fluid atmosphere, consisting of a radiation field and a string fluid. We show that in the appropriate limit when the string energy density goes to zero, the standard result is regained. An exact solution to the generalised boundary condition is found. The generalised boundary condition is extended to hold in the case when the shear is nonvanishing. We demonstrate that our results can be used to model the flow of a string fluid in terms of a diffusion transport process.
Shear-free models for relativistic fluids with heat flow and pressure isotropy.
(2014) Brassel, Byron Perry.; Govender, Gabriel.; Maharaj, Sunil Dutt.
We model the interior dynamics of a relativistic radiating fuid in a nonstatic spher- ically symmetric spacetime. The matter distribution takes the form of an imperfect fuid with a nonvanishing radially directed heat flux. The fluid pressure is isotropic and the spherically symmetric spacetime manifold is described by a shear-free line el- ement. In our investigation, the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. We examine this governing equation by imposing vari- ous forms for these potentials and review classes of physically acceptable models that are applicable in relativistic astrophysics. Several new classes of new exact solutions to the condition of pressure isotropy are also found. A comparison of our solutions with earlier well known results is undertaken. A physical analysis of two of the new models is performed where the spatial and temporal evolution of the matter and grav- itational variables are probed. We demonstrate that the fluid pressure, energy density and heat flux are regular and well behaved for both models throughout the interior, and our results indicate that one of the models is consistent with the well established core-envelope framework for compact stellar scenarios. We also analyse the energy conditions for the radiating fluid and demonstrate consistent behaviour, with only the dominant condition being violated. Finally, an analysis of the relativistic thermody- namics of two solutions is undertaken in the Israel-Stewart theory and the temperature profiles for both the noncausal and causal cases are presented.