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

A mapping ρ: of two Riemannian or pseudo-Riemannian spaces is called aspin mapping if for each geodesic curve γ in M_n its image ρ^oγ is a spin-curve in the space . 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. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 44–47. Original article submitted March 17, 1993.