  According to the Big Bang Theory as we go back in time the Universe becomes
progressively hotter and denser. This leads us to believe that the early
Universe was filled with hot plasma of elementary particles. Among many
questions concerning this phase of history of the Universe there are questions
of existence and fate of magnetic monopoles and primordial black holes. Static
solution of Einstein-Yang-Mills system may be used as a toy model for such a
black hole. Using methods of field theory we will show that its existence and
regularity depend crucially on the presence of fermions around it.
