The Dirac and Rarita-Schwinger equations on traceless Ricci metrics of Taub-NUT type

We construct a traceless Ricci metric of Taub-NUT type whose total mass can be negative. For the Taub-NUT metric and its negative NUT charge counterpart, we prove that the spaces of twistor and parallel spinors coincide and are complex 2-dimensional. We use them to construct L 2 harmonic spinors and Rarita-Schwinger fields. For the traceless Ricci 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.