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

In this paper, 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 two-dimensional. We use them to construct [Formula: see text] 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.