Parametrization of U(N)-monopoles on black holes by the moduli space of holomorphic vector bundles over two-sphere and black hole entropy

摘要

We discuss how to describe U(N) monopoles on the Schwarzschild and Reissner-Nordstrom black holes by the parameters of the moduli space of holomorphic vector bundles over S-2. 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.