Cracking isotropic and anisotropic relativistic spheres
We explore the influence of density fluctuations on isotropic and anisotropic configurations, extending the concept of cracking for general relativistic fluid spheres. This concept, conceived to describe the behaviour of anisotropic matter distributions just after its departure from equilibrium, could provide some insight on potential instabilities and future evolution of relativistic fluids. We have refined the idea of cracking, considering local fluctuations --represented by any function of compact support defined in a closed interval-- and their effect on the state variables and their gradients through "barotropic" equations of state, $P = P(\rho)$ and $P_{\perp}= P_{\perp}(\rho)$. Under this approach it is found that both isotropic and anisotropic models could exhibit cracking (or overturning), and that previously crackable anisotropic models become uncrackable.