U(N)-monopoles on Kerr black hole and its entropy

TL;DR

This paper explores U(N)-monopoles on Kerr black holes using holomorphic vector bundle moduli spaces, providing explicit descriptions for N=2,3 and discussing implications for black hole entropy and fine structure.

Contribution

It introduces a novel description of U(N)-monopoles on Kerr black holes via holomorphic vector bundles, offering explicit forms for N=2,3 and insights into black hole entropy.

Findings

Explicit descriptions for N=2,3 monopoles on Kerr black holes.

Estimates for monopole masses.

Arguments supporting the existence of black hole fine structure and entropy mechanisms.

Abstract

We describe U(N)-monopoles (N > 1) on Kerr black holes by the parameters of the moduli space of holomorphic vector U(N)-bundles over two-sphere 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 a possibility to adduce some reasonings in favour of 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.