Lanczos potential of Weyl field: interpretations and applications

Abstract

An attempt is made to uncover the physical meaning and significance of the obscure Lanczos tensor field which is regarded as a potential of the Weyl field. Despite being a fundamental building block of any metric theory of gravity, the Lanczos tensor has not been paid proper attention as it deserves. By providing an elucidation on this tensor field through its derivation in some particularly chosen spacetimes, we try to find its adequate interpretation. Though the Lanczos field is traditionally introduced as a gravitational analogue of the electromagnetic 4-potential field, the performed study unearths its another feature - a relativistic analogue of the Newtonian gravitational force field. A new domain of applicability of the Lanczos tensor is introduced which corroborates this new feature of the tensor.