Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity

Understand

We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl type $f(Q,T)$ gravity, in which the nonmetricity $Q$ is represented in the standard Weyl form, fully determined by the Weyl vector, while $T$ represents the trace of the matter energy-momentum tensor.

• The effects of the Weyl geometry and of the extra force induced by the nonmetricity-matter coupling are explicitly taken into account.
• The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived.
• As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the nonmetricity-matter coupling, are obtained in the weak field approximation.