On the conformal, concircular, and spin mappings of gravitational fields

A mapping ρ: Mn → Mn of two Riemannian or pseudo-Riemannian spaces is called a spin mapping if for each geodesic curve γ in Mn its image ρoγ is a spin-curve in the space M*n. In gravitational fields spin-curves describe the trajectories of uniformly accelerated particles of constant mass with simultaneous self-rotation. We prove: 1) a conformal mapping is a spin mapping only when it is concircular; 2) every conformal mapping of Einstein space is a spin mapping. The latter makes it possible to give a local representation of the metrics of all gravitational fields that admit spin mappings. ©1998 Plenum Publishing Corporation.