About Twistor Spinors with Zero in Lorentzian Geometry
About Twistor Spinors with Zero in Lorentzian Geometry
We describe the local conformal geometry of a Lorentzian spin manifold $(M,g)$ admitting a twistor spinor $\phi$ with zero. Moreover, we describe the shape of the zero set of $\phi$. If $\phi$ has isolated zeros then the metric $g$ is locally conformally equivalent to a static monopole. In the other …