Parametrization of U(N)-Monopoles on Black Holes by the Moduli Space of Holomorphic Vector Bundles Over Two-Sphere and Black Hole Entropy

Abstract

We discuss how to describe U (N) monopoles on the Schwarzschild and Reissner–Nordström black holes by the parameters of the moduli space of holomorphic vector bundles over S2. For N = 2,3 we obtain such a description in an explicit form as well as the expressions for the corresponding monopole masses. This gives a possibility of adducing some reasonings in favor of existence of both a fine structure for black holes and the statistical ensemble tied with it which might generate the black hole entropy. Also, there arises an analogy with the famous K-theory in topology.