A heuristic procedure is developed to obtain interior solutions of Einstein’s equations for anisotropic matter from known solutions for isotropic matter. Five known solutions are generalized to give solutions with anisotropic sources.
We study the consequences of the existence of a one-parameter group of conformal motions for anisotropic matter, in the context of general relativity. It is shown that for a class of conformal motions (special conformal motions), the equation of state is uniquely determined by the Einstein equations. For spherically symmetric and static distributions of matter we found two analytical solutions of the Einstein equations which correspond to isotropic and anisotropic matter, respectively. Both solutions can be matched to the Schwarzschild exterior metric and possesses positive energy density larger than the stresses, everywhere within the sphere.
The study of the gravitational collapse of a radiating sphere is carried out for times shorter than the effective time of relaxation into diffusion. Using a relativistic version of the Cattaneo equation for the heat flux, we show with an explicit example that processes occurring before relaxation give rise to luminosity profiles which are quite different from the profiles corresponding to vanishing relaxation time, leading thereby to very different patterns of evolution.
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