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

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Jin-Zhao Yang ◽  
Shahab Shahidi ◽  
Tiberiu Harko ◽  
Shi-Dong Liang
Keyword(s):  
Field Approximation ◽  
The Body ◽  
Newtonian Limit ◽  
Raychaudhuri Equation ◽  
Geodesic Deviation ◽  
Weyl Geometry ◽  
Matter Coupling ◽  
Tidal Forces ◽  
Deviation Equation ◽  
Geodesic Deviation Equation

AbstractWe 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.

scholarly journals k-Jet field approximations to geodesic deviation equations

2018 ◽  
Vol 15 (12) ◽  
pp. 1850199
Author(s):  
Ricardo Gallego Torromé ◽  
Jonathan Gratus
Keyword(s):  
Differential Equations ◽  
Tangent Bundle ◽  
Jacobi Equation ◽  
Smooth Manifold ◽  
Specific Class ◽  
Coordinate Transformations ◽  
Geodesic Deviation ◽  
Deviation Equation ◽  
Geodesic Deviation Equation ◽  
Deviation Functions

Let [Formula: see text] be a smooth manifold and [Formula: see text] a semi-spray defined on a sub-bundle [Formula: see text] of the tangent bundle [Formula: see text]. In this work, it is proved that the only non-trivial [Formula: see text]-jet approximation to the exact geodesic deviation equation of [Formula: see text], linear on the deviation functions and invariant under an specific class of local coordinate transformations, is the Jacobi equation. However, if the linearity property on the dependence in the deviation functions is not imposed, then there are differential equations whose solutions admit [Formula: see text]-jet approximations and are invariant under arbitrary coordinate transformations. As an example of higher-order geodesic deviation equations, we study the first- and second-order geodesic deviation equations for a Finsler spray.

scholarly journals Erratum to: Geodesic deviation equation in f(R) gravity

2015 ◽  
Vol 47 (10) ◽  
Author(s):  
Alejandro Guarnizo ◽  
Leonardo Castañeda ◽  
Juan M. Tejeiro
Keyword(s):  
Geodesic Deviation ◽  
Deviation Equation ◽  
Geodesic Deviation Equation

scholarly journals Tidal forces in the charged Hayward black hole spacetime

2020 ◽  
Vol 29 (11) ◽  
pp. 2041014
Author(s):  
Haroldo C. D. Lima ◽  
Luís C. B. Crispino
Keyword(s):  
Black Hole ◽  
Initial Conditions ◽  
Radial Coordinate ◽  
Geodesic Deviation ◽  
Regular Black Hole ◽  
Tidal Forces ◽  
Deviation Equation ◽  
Spacetime Curvature ◽  
Black Hole Spacetime ◽  
Electrically Charged

Tidal forces produced by black holes are an important result of General Relativity related to the spacetime curvature tensor. Among the astrophysical implications of tidal forces, the tidal disruption events stand out. We analyze the tidal forces in the spacetime of an electrically charged Hayward regular black hole, obtaining the components of the tidal tensor and the geodesic deviation equation. We find that the radial and angular tidal forces may vanish and change sign unlike in the Schwarzschild spacetime. We note that tidal forces are finite at the origin of the radial coordinate in this regular black hole spacetime. We obtain the geodesic deviation vector for a body constituted of dust infalling towards the black hole with two different initial conditions.

scholarly journals A scalar geodesic deviation equation and a phase theorem

1983 ◽  
Vol 6 (4) ◽  
pp. 795-802 ◽  
Author(s):  
P. Choudhury ◽  
P. Dolan ◽  
N. S. Swaminarayan
Keyword(s):  
Gravitational Field ◽  
Phase Shift ◽  
Relative Motion ◽  
Plane Waves ◽  
Relative Energy ◽  
Positive Definite ◽  
Geodesic Deviation ◽  
Deviation Equation ◽  
Test Particles ◽  
Geodesic Deviation Equation

A scalar equation is derived forη, the distance between two structureless test particles falling freely in a gravitational field:η¨+(K−Ω2)η=0. An amplitude, frequency and a phase are defined for the relative motion. The phases are classed as elliptic, hyperbolic and parabolic according asK−Ω2>0,<0,=0.In elliptic phases we deduce a positive definite relative energyEand a phase-shift theorem. The relevance of the phase-shift theorem to gravitational plane waves is discussed.

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