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The generalized Lemaitre-Tolman-Bondi solutions with nonzero pressure in modeling the cosmological black holes

In this work we have obtained the set of new exact solutions of the Einstein equations that generalize the known Lemaitre-Tolman-Bondi solution for the certain case of nonzero pressure under zero spatial curvature. These solutions are pretending to describe the black hole immersed in the nonstatic cosmological background and give a possibility to investigate the problems concerning the effects of the cosmological expansion in gravitationally bounded systems. They may also be used as a seed models in the problem of structure formation in the universe at the epoch of matter and radiation decoupling. It was shown that each of the solutions obtained contains either the Reissner-Nordstrom or the Schwarzschild black hole in the central region of the space. It is demonstrated that the approach of the mass function use in solving the Einstein equations allows clear physical interpretation of the resulting solutions that is of much benefit to any their further application.