Sound speeds, cracking and the stability of self-gravitating anisotropic compact objects

Using the concept of cracking we explore the influence that density fluctuations and local anisotropy have on the stability of local and non- local anisotropic matter configurations in general relativity. This concept, conceived to describe the behavior of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of self-gravitating compact objects. We show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions. In fact, it is found that these regions could occur when, at a particular point within the distribution, the tangential speed of sound is greater than the radial one.