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A gauge-invariant version of the Stachel string cloud model is presented. Some formal aspects as well as the energy conditions for the model are studied. The general solution to Einstein's equations for a cloud of strings with spherical, plane, and a particular case of cylindrical symmetry are studied. The solution with spherical symmetry is used to construct a double-layer model of a star.
Patricio S. Letelier (Sat,) studied this question.