Lanczos potential of Weyl field: interpretations and applications Ram Gopal Vishwakarma* Unidad Acade´mica de Matema´ticas Universidad Auto´noma de Zacatecas, Zacatecas, ZAC, Mexico 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 ap- plicability of the Lanczos tensor is introduced which corroborates this new feature of the arXiv:2103.00311v2 [gr-qc] 1 Apr 2021 tensor. PACS: 04.20.Cv, 04.20.-q, 04.30.-w, 95.30.Sf Keywords: Lanczos tensor, potential of Weyl tensor, gravitational waves, gravitational collapse. 1 Introduction General Relativity (GR), which constitutes the current description of gravitation in modern physics, appears to be afflicted with at least two major difficulties. Firstly, it shows an intrin- sic difficulty in its unification with the rest of physics, which is perhaps the most profound foundational problem in physics. Secondly, its cosmological application - the ΛCDM model - faces challenges on both theoretical and observational grounds, despite its overall success and *E-mail address:
[email protected] 2 Ram Gopal Vishwakarma simplicity.