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arXiv · 2409.16335

n-dimensional Weyl conformal tensor in a 4-index gravitational field theory

Frédéric Moulin
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Abstract

The Weyl conformal tensor is the traceless component of the Riemann tensor and therefore, as is known, the information it contains does not appear explicitly in Einstein's equation. Following a rigorous mathematical treatment based on the variational principle, we will suggest that there exists a four-index gravitational field equation linearly containing the Weyl tensor closely related to a tidal gravitational field tensor whose components will be calculated. The new degrees of freedom, introduced via the n-dimensional Weyl tensor, will therefore clearly appear as additional constraints on the metric and we will demonstrate, among other things, that the cosmological constant appears as a natural solution of the four-index theory in the form of an integration constant which therefore does not need to be introduced ad hoc into a Lagrangian.

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Frédéric Moulin. 2025-04-16. n-dimensional Weyl conformal tensor in a 4-index gravitational field theory. https://doi.org/10.1016/j.aop.2025.170026

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