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

Sound speeds, cracking and stability of self-gravitating anisotropic compact objects.\nAbstract\n\nUsing the the concept of cracking we explore the influence of 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 behaviour of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of selfgravitating compact objects. We show that potentially unstable regions within a configuration can be identify as a function of the difference of propagations of sound along tangential and radial directions. In fact, it is found…