Generalization of Einstein's gravitational field equationsFr\'ed\'eric Moulinhttps://arxiv.org/abs/2405.03698 https://a…

Generalization of Einstein's gravitational field equationsThe Riemann tensor is the cornerstone of general relativity, but as everyone knows it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show th…