: The final report covering the research performed under the Air Force Office of Scientific Research by the Dallas relativity group, summarizes information on personnel involved, on the scientific work done, and on the results obtained in the four years of the grant's duration. Topics investigated were in areas of General relativity, cosmology, and electrodynamics.

Exact Solutions of Einstein's Field Equations.

In this study we generate the matching conditions for a spherically symmetric radiating star in the presence of shear. Two new exact solutions to the Einstein field equations are presented which model a relativistic radiating sphere. We examine the role of anisotropy in the thermal evolution of a radiating star undergoing continued dissipative gravitational collapse in the presence of shear. Our model was the first study to incorporate both shear and pressure anisotropy, and these results were published in 2006. The physical viability of a recently proposed model of a shear-free spherically symmetric star undergoing gravitational collapse without the formation of a horizon is investigated. These original results were published in 2007. The temperature profiles of both models are studied within the framework of extended irreversible thermodynamics.

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Dynamics of dissipative gravitational collapse.

In this thesis we model spherically symmetric radiating stars dissipating energy in the form of a radial heat flux. We assume that the spacetime for the interior matter distribution is shear-free. The junction conditions necessary for the matching of the exterior Vaidya solution to an interior radiating line element are obtained. In particular we show that the pressure at the boundary of the star is nonvanishing when the star is radiating (Santos 1985). The junction conditions, with a nonvanishing cosmological constant, were obtained. This generalises the results of Santos (1985) and we believe that this is an original result. The Kramer (1992) model is reviewed in detail and extended. The evolution of this model depends on a function of time which has to satisfy a nonlinear second order differential equation. We solve this differential equation in general and thereby completely describe the temporal behaviour of the Kramer model. Graphical representations of the thermodynamical and gravitational variables are generated with the aid of the software package MATHEMATICA Version 2.0 (Wolfram 1991). We also analyse two other techniques to generate exact solutions to the Einstein field equations for modelling radiating stars. In the first case the particle trajectories are assumed to be geodesics. We indicate how the model of Kolassis et al (1988) may be extended by providing an ansatz to solve a second order differential equation. In the second case we review the models of de Oliveira et al (1985, 1986, 1988) where the gravitational potentials are separable functions of the spatial and temporal coordinates.

Megandren. Govender

Papers

Radiating solutions with heat flow in general relativity.