Relativistic potential of Weyl: a gateway to quantum physics in the presence of gravitation?

TL;DR

This paper explores the Lanczos tensor, revealing its quantum signatures and challenging its traditional interpretation as a gravitational potential, thus offering new insights into quantum aspects of gravity within metric theories.

Contribution

It derives explicit expressions for the Lanczos tensor in specific spacetimes and uncovers its quantum signatures, providing a novel perspective on gravity's geometric nature.

Findings

Lanczos tensor does not serve as a gravitational potential

The tensor exhibits quantum signatures

Provides new insights into quantum gravity

Abstract

The well-noted correspondence between gravitation and electrodynamics emphasizes the importance of the Lanczos tensor -- the potential of the Weyl tensor -- which is an inherent structural element of any metric theory of gravity formulated in a 4-dimensional pseudo Riemannian spacetime. However, this ingenious discovery has gone largely unnoticed. We elucidate this important quantity by deriving its expressions in some particularly chosen spacetimes and try to find out what it represents actually. We find out that the Lanczos potential tensor does not represent the potential of the gravitational field, as is ascertained by various evidences. Rather, it is enriched with various signatures of quantum character, which provides a novel insight into the heart of a geometric embodiment of gravity.