## 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.