U(N)-MONOPOLES ON KERR BLACK HOLE AND ITS ENTROPY

Abstract

We describe U(N)-monopoles (N>1) on Kerr black holes using the parameters of the moduli space of holomorphic vector U(N)-bundles over [Formula: see text] with the help of the Grothendieck splitting theorem. For N = 2,3 we obtain this description in an explicit form as well as the estimates for the corresponding monopole masses. This gives us a possibility to adduce some reasonings in favor of the existence of both a fine structure for Kerr black holes and the statistical ensemble tied with it which might generate the Kerr black hole entropy.