Dissipative gravitating systems.
In this thesis we investigate the effect of shear on radiating stars undergoing gravitational collapse. The interior spacetime is described by the most general spherically symmetric line element in the absence of rotation. The energy momentum tensor for the stellar interior is taken to be an anisotropic fluid with heat flux. The thermodynamics of a relativistic fluid is reviewed for the Eckart and causal theories. Since the star is radiating energy to the exterior in the form of a radial heat flux, the atmosphere is described by Vaidya's outgoing solution. We provide the matching conditions required for the continuity of the momentum flux across the boundary, which determines the temporal evolution junction conditions for the metric functions. We provide a general method to obtain shearing solutions of the Einstein field equations describing a radiating, collapsing sphere. A particular exact solution satisfying the boundary condition and field equations is found. The validity of this specific model is investigated by employing a causal heat transport equation which yields the temperature profile within the stellar core. The energy conditions are studied and yield interesting features of this particular model which are absent in the shear-free case.