LOCAL ANISOTROPY IN SELF-GRAVITATING SYSTEMS

We review and discuss possible causes for the appearance of local anis otropy (principal stresses unequal) in self-gravitating systems and pr esent its main consequences. We consider both Newtonian and general re lativistic examples. The results emerging from the stability analysis hint at the potential relevance of local anisotropy in the evolution o f self-gravitating objects. In this respect particular attention is de voted to the Jeans instability criterion and to the occurrence of crac king in anisotropic spheres. A selection of solutions to Einstein equa tions for anisotropic matter is analyzed. The specific consequences de rived from local anisotropy in these solutions, are exhibited. The dif ferences between two different definitions of energy, within a slowly evolving distribution of anisotropic fluid, are discussed in detail. T he conspicuous role played by the Weyl and shear tensors and their rel ationship with anisotropy of the fluid are brought out.