Local anisotropy in self-gravitating systems

Abstract We review and discuss possible causes for the appearance of local anisotropy (principal stresses unequal) in self-gravitating systems and present its main consequences. We consider both Newtonian and general relativistic examples. The results emerging from the stability analysis hint at the potential relevance of local anisotropy in the evolution of self-gravitating objects. In this respect particular attention is devoted to the Jeans instability criterion and to the occurrence of cracking in anisotropic spheres. A selection of solutions to Einstein equations for anisotropic matter is analyzed. The specific consequences derived from local anisotropy in these solutions, are exhibited. The differences between two different definitions of energy, within a slowly evolving distribution of anisotropic fluid, are discussed in detail. The conspicuous role played by the Weyl and shear tensors and their relationship with anisotropy of the fluid are brought out.