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.
Highlights
General relativity (GR), which constitutes the current description of gravitation in modern physics, appears to be afflicted with at least two major difficulties
With the values of this tensor derived in these sections, we explore what physical information this potential tensor may convey in a physical situation
Conformal symmetry plays an important role in field theories including gravity and leads to interesting insights about the physical phenomena related to the dynamics of spacetime
Summary
General relativity (GR), which constitutes the current description of gravitation in modern physics, appears to be afflicted with at least two major difficulties. It has been shown that the Minkowski spacetime admits non-trivial values of the Lanczos potential [3,4], proclaiming that the Lanczos potential is a property of spacetime itself rather than an outcome of a particular theory of gravity This simple but farreaching insight of mathematical and philosophical value, revolutionizes our views on the foundational nature of spacetime itself indicating towards an important substantive nature of spacetime and its geometry. After exemplifying this tensor field by deriving its values in various spacetimes we discover some possible applications thereof in some gravitational phenomena This may help to assign an adequate physical interpretation to the tensor
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