Cracking of Homogeneous Self-Gravitating Compact Objects Induced by Fluctuations of Local Anisotropy

Abstract

We discuss the effect that small fluctuations of local anisotropy (principal stresses unequal) may have on the occurrence of cracking in spherical compact objects. Two families of homogeneous fluid distributions are considered. For both it is shown that departures from equilibrium may lead to the appearance of cracking, only if fluctuations of local anisotropy are allowed. The case of fluctuations in an initially locally isotropic (perfect fluid) configuration deserves particular attention.