MG14 - Talk detail

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We revisit and extend the cracking (or overturning) methodology, -developed by Herrera et al- to determine instabilities in spherical configurations of neutral and charged matter in General Relativity, we first consider isotropic and anisotropic spherical configurations governed by barotropic equations of state, and study a general radial perturbation of the density, which has a dependency on the radial coordinate and affects the pressures and the gradient of the radial pressure. The perturbation may be defined by a compact support function, so the perturbation occurs in a finite and small region of the configuration where the function is defined. In the second part, we have an anisotropic spherical fluid with electric charge, governed by barotropic equations of state and where the charge has a dependency with the density, thereafter the perturbation in the density has an effect in the charge as well as in the other variables. In both cases, general expressions of the distribution of radial forces that appear in the system, due to the perturbation of the density, were found. In both cases the term of the perturbation is factorized so the appearance of cracking and overturning can be studied in a independent way form the form of the perturbation. Some models of neutral and charged, isotropic and anisotropic relativistic spheres proposed in the literature are studied and some instabilities due to cracking are found, our extension of the cracking framework has shown that even isotropic configurations can exhibit cracking instabilities. A case of cracking is found in an isotropic charged model and an example of overturning is found in an anisotropic charged model.

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