The mass function method for obtaining the exact solutions

In this work it is shown that rewriting the Einstein equations in terms of mass function, which is one of four algebraic invariants for spherically symmetric metrics, it is possible to obtain the exact solutions of these equations in tangibly more simple way. The mass function method was applied for obtaining known exact solutions for the empty space as well as new solutions were obtained, for example, the solution in Gaussian coordinate system and Kruskal-Szekeres generalized solution. It is shown that with the mass function method it is much simpler to obtain Tolman-Bondi solutions, and new exact Friedman-like solution were obtained for the case of nonzero pressure. Besides the solutions for Schwarzschild black holes were considered and it was shown that it such black holes necessarily contain non-baryonic matter. The exact solutions for the black hole embedded into the dust matter universe were obtained.