Showing papers on "Geodesic deviation published in 2010"
TL;DR: Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe as mentioned in this paper, and its main current applications and representative results achieved so far.
Abstract: Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.
404 citations
TL;DR: In this article, the authors deal with the design and on-ground testing approaches of the injection in geodesic conditions phase developed in the frame of some scientific space missions, chosen as meaningful cases.
21 citations
TL;DR: In this article, the radial motion along null geodesics in static charged black hole space-times, in particular, the Reissner-Nordstrom and stringy charged black holes, was studied.
Abstract: The radial motion along null geodesics in static charged black hole space–times, in particular, the Reissner–Nordstrom and stringy charged black holes, are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space–times are investigated. We found that the radius of circular photon orbits in both charged black holes are different and differ from that given in Schwarzschild space–time. We studied the physical effects of the gravitational field between two test particles in stringy charged black hole and compared the results with that given in Schwarzschild and Reissner–Nordstrom black holes.
19 citations
01 May 2010
TL;DR: In this article, the Geodesic Deviation Equation (GDE) for the Friedmann Robertson Walker (FRW) universe and the equation for Bianchi type I model were compared.
Abstract: We present the Geodesic Deviation Equation (GDE) for the Friedmann Robertson Walker(FRW) universe and we compare it with the equation for Bianchi type I model. We justify consider this cosmological model due to the recent importance the Bianchi Models have as alternative models in cosmology. The main property of these models, solutions of Einstein Field Equations (EFE) is that they are homogeneous as the FRW model but they are not isotropic. We can see this because they have a non-null Weyl tensor, which is zero for FRW model. We study some consequences of this Weyl tensor in the GDE.
14 citations
TL;DR: The relative classical motion of membranes is governed by the equation (wβ cα crβa)a = Rδγβαrgbxδapaγ, where w is the hessian as discussed by the authors.
Abstract: The relative classical motion of membranes is governed by the equation (wβ cα crβa)a = Rδγβαrgbxδapaγ, where w is the hessian. This is a generalization of the geodesic deviation equation and can be derived from the lagrangian p · ṙ. Quantum mechanically the picture is less clear. Some quantizations of the classical equations are attempted so that the question as to whether the Universe started with a quantum fluctuation can be addressed.
7 citations
TL;DR: In this article, the singularity in geodesic surface congruences is assumed to exist in a conformally symmetric manifold, and the Jacobi fields of the geodeic surface deviation equations are computed and observed.
Abstract: Using the Nambu–Goto string action in the space of the surfaces spanned by closed strings in a spacetime manifold, we investigated the geodesic surface equation in the space of surfaces joining two given strings and the geodesic surface deviation equation in geodesic surface congruence which yields a Jacobi field along a given geodesic surface, and singularities in geodesic surface congruences. In this paper, assuming that the singularity exists in geodesic surface congruences in a conformally symmetric manifold, we compute the Jacobi fields of the geodesic surface deviation equations and observe them.
6 citations
Posted Content•
TL;DR: In this paper, it was shown that the necessary and sucient condition for erecting locally inertial coordinates at a point p of a U 4 -space and assuring the validity of the equivalence principle at that point, is the vanishing at p of the symmetric part of the contortion tensor, which does not require a vanishing torsion, but only a totally an- tisymmetric one.
Abstract: We show that the necessary and sucient condition for erecting locally inertial coordinates at a point p of a U 4 -space, and the- refore assuring the validity of the equivalence principle at that point, is the vanishing at p of the symmetric part of the contortion tensor. This fact does not demand a vanishing torsion, but only a totally an- tisymmetric one. As an application, we derive the geodesic deviation equation; and prove the compatibility with the Newtonian limit. The problem of the validity of the equivalence principle (EP) in gra- vity theories with torsion and zero non-metricity (1), (2), has been discus- sed by several authors (3), (4), (5). The strategy of these authors consisted in showing the existence of local basis or normal frames such that, with respect to them, all components of the linear connection, which gives the gravitational "force", vanish at a given point of the manifold (von der Heyde, Hartley) or also in a neighborhood of the point (Iliev). The pur- pose of the present article is to show that a particularly simple change of coordinates, can also maintain the validity of the EP in the presence of torsion, with the only restriction of this being totally antisymmetric. This is allowed by the structure of the geodesic equation. Using the fact that only the symmetric part of the connection intervenes in this equation, in section 2 we show that a necessary and sucient condition for the vanishing of the first derivatives of the metric is the vanishing
5 citations
Posted Content•
TL;DR: In this article, the authors show how the systematics of the gravitational correlation can be used for calibration and de-trending which can significantly increase the confidence level of high precision experiments.
Abstract: Newtonian gravitation is non-radiative but is extremely pervasive and penetrates equally into every media because it cannot be shielded. The extra terrestrial fgravity is responsible for earth's trajectory. However its correlation or geodesic deviation is manifested as semi-diurnal and diurnal tides. Tidal signals, A(t) are temporal modulations in the field differential which can be observed in a wide variety of natural and laboratory situations. A(t) is a quasi-static, low frequency signal which arises from the relative changes in positions of the detector and source and is not part of the electromagnetic spectrum. Isaac Newton was the first to recognize the importance of tides in astrometry and attempetd to estimate lunar mass from ocean tides. By a case study we show, how the systematics of the gravitational correlation can be used for calibration and de-trending which can significantly increase the confidence level of high precision experiments. A(t) can also be used to determine the distribution of celestial masses independently of the "1-2-3" law. Guided by modern advances in gravity wave detectors we argue that it is important to develop high precision accelerometry. With a resolution of about a nano-m it will be possible to determine solar system masses and detect the SMBH at the center of our galaxy. Observations of the gravitational correlation can potentially open up yet to be explored vistas of the cosmos.
1 citations
TL;DR: In this paper, the authors extended the work of Kerner et al. to the presence of scalar fields in the Kaluza-Klein model and derived an exact law for such a behaviour.
Abstract: In the work of Kerner et al. (Phys Rev D 63:027502, 2001) the problem of the geodesic deviation in a 5D Kaluza–Klein background is faced. The 4D space–time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the q/m conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza–Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case \({\phi=1}\) is considered, while it shows some departures in the general case. The novelty due to the presence of \({\phi}\) is that the variation of the q/m between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.
1 citations
TL;DR: In this paper, the Geodesic Deviation Equation (GDE) in metric f(R) gravity was studied and an equivalent expression to the Dyer-Roeder equation in General Relativity in the context of gravity was given.
Abstract: In this paper we study the Geodesic Deviation Equation (GDE) in metric f(R) gravity. We start giving a brief introduction of the GDE in General Relativity in the case of the standard cosmology. Next we generalize the GDE for metric f(R) gravity using again the FLRW metric. A generalization of the Mattig relation is also obtained. Finally we give and equivalent expression to the Dyer-Roeder equation in General Relativity in the context of f(R) gravity.