M. Sc. University of KwaZulu-Natal, Durban 2014.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
