Analysis of Local Anisotropy Fluctuations in Compact Objects

Mathematical modeling within the framework of the general theory of relativity has been used to explain the behavior and structure of massive objects as neutron stars, quasars, black holes, pulsars and white dwarfs and requires finding the exact solutions of the Einstein-Maxwell system. In this paper we study the effects induced by fluctuations of local anisotropy in a new family of anisotropic solutions depending on a parameter, with a specific value that provides a radial pressure having the same functional dependence on the radial coordinate as the Schwarzschild solution. It is shown the effect the functional dependence on the radial coordinate has in the occurrence of cracking within the sphere when anisotropy fluctuations are allowed.