Single Kerr-Schild Metric for Taub-NUT Instanton

TL;DR

This paper demonstrates that the Taub-NUT instanton metric can be expressed as a Kerr-Schild metric via a complex coordinate transformation, revealing connections to classical double copy and the Newman-Janis algorithm.

Contribution

It introduces a Kerr-Schild form of the Taub-NUT instanton and explores its implications for classical double copy correspondence and related gravitational-electromagnetic analogies.

Findings

Taub-NUT instanton maps to Kerr-Schild metric

Three versions of classical double copy are identified

Connection to Newman-Janis algorithm is discussed

Abstract

It is shown that a complex coordinate transformation maps the Taub-NUT instanton metric to a Kerr-Schild metric. This metric involves a semi-infinite line defect as the gravitational analog of the Dirac string, much like the original metric. Moreover, it facilitates three versions of classical double copy correspondence with the self-dual dyon in electromagnetism, one of which involving a nonlocal operator. The relevance to the Newman-Janis algorithm is briefly noted.