Cracking and Stability of Non-Rotating Relativistic Spheres with Anisotropic Internal Stresses

The stability of static uncharged spheres with anisotropic internal stresses is studied in general relativity. It has been noticed that pressure anisotropy plays an important role for stability of stellar structure. It is shown that radial profile of the stress anisotropy can be considered to decide potentially stable/unstable regions. Finally, pontentially stable/unstable regions of two known models of relativistic star have been examined.