English

On the Weyl Tensor for a Curved Spacetime Endowed with a Torsionful Affinity

General Relativity and Quantum Cosmology 2025-01-20 v4

Abstract

We transcribe into the framework of the torsionful version of the {\epsilon}-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.

Keywords

Cite

@article{arxiv.2409.07364,
  title  = {On the Weyl Tensor for a Curved Spacetime Endowed with a Torsionful Affinity},
  author = {J. G. Cardoso},
  journal= {arXiv preprint arXiv:2409.07364},
  year   = {2025}
}

Comments

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