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 non-metricity 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 non-metricity–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 non-metricity–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.
Highlights
The twentieth century has seen the birth of General Relativity (GR) and of Quantum Mechanics (QM), which are considered as the most two successful theories describing the nature and properties of the physical world, on scales ranging from the microscopic to the cosmological one
To allow for the generation of long-range forces and simultaneously passing the Solar System test, in [36,37,38,39,40] a new approach to gravitational effects was proposed. In this theory, called Hybrid Metric-Palatini Gravity, the Einstein–Hilbert action is supplemented with a correction term inspired by the Palatini formulation. Another interesting and important modification of gravity is the inclusion of a non-minimal coupling of geometry and matter into the action [41,42,43,44,45,46,47,48], by using arbitrary functions of the scalar curvature and Lagrangian density of matter (in the f (R, Lm) gravity theory [47]), or by considering a gravitational Lagrangian of the form f (R, T ) [48], where T is the trace of the matter energy–momentum tensor
The main goal of the present paper is to investigate some fundamental properties of the motion of test particles in the Weyl type f (Q, T ) gravity theory, introduced in [104]
Summary
The twentieth century has seen the birth of General Relativity (GR) and of Quantum Mechanics (QM), which are considered as the most two successful theories describing the nature and properties of the physical world, on scales ranging from the microscopic to the cosmological one. To allow for the generation of long-range forces and simultaneously passing the Solar System test, in [36,37,38,39,40] a new approach to gravitational effects was proposed In this theory, called Hybrid Metric-Palatini Gravity, the Einstein–Hilbert action is supplemented with a correction term inspired by the Palatini formulation. Another interesting and important modification of gravity is the inclusion of a non-minimal coupling of geometry and matter into the action [41,42,43,44,45,46,47,48], by using arbitrary functions of the scalar curvature and Lagrangian density of matter (in the f (R, Lm) gravity theory [47]), or by considering a gravitational Lagrangian of the form f (R, T ) [48], where T is the trace of the matter energy–momentum tensor. In the present section we briefly review the fundamentals of the Weyl geometry, and of the Weyl-type f (Q, T ) gravity
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