On the Weyl Tensor for a Curved Spacetime Endowed with a Torsionful Affinity
arXiv:2409.07364 · doi:10.1016/j.aop.2025.169926
Abstract
We transcribe into the framework of the torsionful version of the ε-formalism of Infeld and van der Waerden the world definition of the Weyl tensor for a curved spacetime that occurs in the realm of Einstein-Cartan's theory. The resulting expression shows us that it is not possible to attain any general condition for conformal flatness in such a spacetime even if wave functions for gravitons are eventually taken to vanish identically. A short discussion on the situation concerning the limiting case of general relativity is presented thereafter.
Some modifications have been made to Section 2 of the article, in connection with a reviewer's suggestion. The current version has been accepted for publication in the Annals of Physics journal. An acknowledgement byline has likewise been introduced