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We describe the departure from equilibrium of matter distributionsrepresenting sources for a class of Weyl metric. It is shown that, forextremely high gravitational fields, slight deviations from spherical symmetrymay enhance the stability of the system weakening thereby its tendency to acatastrophic collapse. For critical values of surface gravitational potential,in contrast with the exactly spherically symmetric case, the speed of enteringthe collapse regime decreases substantially, at least for specific cases.Comment: 26 pages Latex, a shortened version to appear in Astr.Space.Sc

Non spherical sources of strong gravitational fields out of hydrostatic equilibrium