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 andReissner-Nordstr\"om black holes by the parameters of the moduli space ofholomorphic vector bundles over S^2. For N = 2,3 we obtain such a descriptionin an explicit form as well as the expressions for the corresponding monopolemasses. This gives a possibility to adduce some reasonings in favour ofexistence of both a 'fine structure' for black holes and the statisticalensemble tied with it which might generate the black hole entropy. Also therearises some analogy with the famous K-theory in topology.