Abstract

In electromagnetism, the Faraday tensor [Formula: see text] can be constructed from the vector potential [Formula: see text], it is possible to add term to the Lagrangian depending on [Formula: see text] but not its derivatives called Chern–Simons terms. In gravitation, the Weyl tensor [Formula: see text] can be constructed from the Lanczos potential [Formula: see text], I pursue the analogy to see if terms of Chern–Simons form can be added to the Lagrangian. A new tensor [Formula: see text] is introduced which is constructed from the Lanczos potential and is of the same form as that of the Weyl tensor [Formula: see text] expressed in terms of the Lanczos potential except that covariant differentiation is replaced by transvection with a vector [Formula: see text]. The new tensor has associated invariants [Formula: see text] and [Formula: see text], the first of these can be interpreted as a Chern–Simons term for Weyl [Formula: see text] gravity. Both invariants allow various tensors to be constructed and some of their properties are investigated by using exact examples.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.