Radiating solutions with heat flow in general relativity.

Abstract

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.