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

TL;DR

This paper explores how U(N)-monopoles on black holes can be characterized using the moduli space of holomorphic vector bundles over a sphere, providing insights into black hole entropy and potential fine structure.

Contribution

It offers an explicit description of U(N)-monopoles on black holes for N=2,3 and links these to black hole entropy and topological K-theory.

Findings

Explicit formulas for monopole masses for N=2,3

Proposal of a 'fine structure' for black holes

Analogy with K-theory in topology

Abstract

We discuss how to describe U(N)-monopoles on the Schwarzschild and Reissner-Nordstr\"om 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 to adduce some reasonings in favour 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 some analogy with the famous K-theory in topology.