Singular Monopoles and Gravitational Instantons

TL;DR

This paper models specific gravitational instantons using moduli spaces of solutions to Bogomolny equations, providing explicit twistor descriptions and Kähler potentials for these instantons.

Contribution

It introduces a novel approach to modeling A_k and D_k gravitational instantons via moduli spaces and derives their twistor descriptions and Kähler potentials.

Findings

Explicit twistor descriptions of A_k and D_k instantons

Derived Kähler potentials for these instantons

Enhanced understanding of their geometric structure

Abstract

We model A_k and D_k asymptotically locally flat gravitational instantons on the moduli spaces of solutions of U(2) Bogomolny equations with prescribed singularities. We study these moduli spaces using Ward correspondence and find their twistor description. This enables us to write down the K\"ahler potential for A_k and D_k gravitational instantons in a relatively explicit form.