Lanczos potential of Weyl field: interpretations and applications

TL;DR

This paper explores the physical meaning of the Lanczos tensor, revealing it as both a gravitational potential and a relativistic analogue of the Newtonian gravitational force, expanding its interpretative framework.

Contribution

It provides new interpretations of the Lanczos tensor, including its role as a relativistic gravitational force analogue, and explores its applications in specific spacetimes.

Findings

Lanczos tensor acts as a potential of the Weyl field.

It can be interpreted as a relativistic Newtonian gravitational force.

New applications of the Lanczos tensor are proposed.

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.