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We show that the mass function method makes it much easier to obtain theexact solutions of Einstein equations. The known solutions for empty space andfor the universe filled with dust-like matter are considered from the point ofview of the method and new exact solutions are obtained. Generalized solutionsfor the Schwarzschild type black holes are considered. It is shown that suchblack holes always contain non-baryonic matter. New exact solution for theblack hole embedded into dust matter cosmological background is obtained.

The mass function method for obtaining exact solutions of Einstein equations