The Dirac and Rarita-Schwinger equations on scalar flat metrics of Taub-NUT type

TL;DR

This paper constructs scalar flat Taub-NUT type metrics with negative mass, analyzes the Dirac and Rarita-Schwinger equations on these backgrounds, and finds explicit solutions in special cases, revealing insights into harmonic spinors and fields.

Contribution

It introduces new scalar flat Taub-NUT type metrics with negative mass and provides explicit solutions to Dirac and Rarita-Schwinger equations on these geometries.

Findings

Existence of scalar flat Taub-NUT type metrics with negative mass.

Explicit solutions to Dirac and Rarita-Schwinger equations in special cases.

Identification of harmonic spinors and Rarita-Schwinger fields on these metrics.

Abstract

We construct a scalar flat metric of Taub-NUT type whose total mass can be negative. The standard Taub-NUT metric and its negative NUT charge counterpart serve as particular examples, for which the complex 2-dimensional space of parallel spinors gives rise to $L^2$ harmonic spinors and Rarita-Schwinger fields. For the scalar flat Taub-NUT type metric, we study the Dirac and Rarita-Schwinger equations by separating them into angular and radial equations, and obtain explicit solutions in certain special cases.