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

TL;DR

This paper explores how Weyl-type $f(Q,T)$ gravity affects geodesic deviation, Raychaudhuri equation, and tidal forces, revealing modifications to Newtonian gravity and astrophysical phenomena like the Roche limit.

Contribution

It introduces the effects of Weyl geometry and matter coupling into geodesic and tidal force equations, providing new insights into gravitational behavior in this modified gravity theory.

Findings

Derived the generalized Poisson equation with Weyl corrections.

Analyzed the impact of nonmetricity-matter coupling on tidal forces.

Calculated the Roche limit within Weyl $f(Q,T)$ gravity.

Abstract

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. The tidal motion of test particles is directly influenced by the gradients of the extra force, and of the Weyl vector. As a concrete astrophysical example we obtain the expression of the Roche limit (the orbital distance at which a satellite begins to be tidally torn apart by the body it orbits) in the Weyl type $f(Q,T)$ gravity.