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(ρ) and P⊥= P⊥(ρ). Under this approach it is found that both isotropic and that previous results for cracking (and overturning) instabilities on anisotropic matter configurations has to be revised.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author