Single Kerr-Schild Metric for Taub-NUT Instanton

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.

arXiv comment(v1) 9 pages, 2 figures; (v2) 10 pages, 2 figures, note added; (v3) 10 pages, 2 figures, added appendix; (v4) 8 pages, 2 figures, journal submitted version;