The mass function method for obtaining exact solutions of Einstein equations

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