Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb

doi:10.1088/1361-6382/aa5a63

Cited by 22 publications

(15 citation statements)

References 59 publications

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“…Physically, we do expect k to be independent of m, and this is reflected by the independence of κ. However, expressing k using (29) and considering κ to be of order O(1) or less ensures that the parameters lie within the regime m > m crit , and we remain within the shaded region of Fig. 4.…”

Section: Lensing In the Schwarzschild-de Sitter Spacetimementioning

confidence: 73%

“…we can now attempt to find the approximate bending angle in the general case where k = 0 and γ = 0. Using (29) and (33) in (26) and performing an expansion in m/r 0 , we If we further expand in terms of κ and w, to leading order in each parameter, we have…”

Section: Lensing In the Mk Spacetime With K =mentioning

confidence: 99%

“…Villanueva and Olivares [28] solved the geodesic equations exactly to provide the coordinate deflection angle. In their analysis of MK geodesics, Hoseini et al [29] provided the deflection angle under the Rindler-Ishak formalism. However, the focus of their work was on the geodesic structure of the MK metric, and it has yet to draw any conclusions as to the sign of γ pertaining to lensing observations.…”

Section: Introductionmentioning

confidence: 99%

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Exact gravitational lensing in conformal gravity and Schwarzschild–de Sitter spacetime

Lim

Wang

2017

Phys. Rev. D

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An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small bending-angle approximation for a lens system where the source, lens and observer are co-aligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to non-existent null trajectories. The linear coefficient γ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by General Relativity for small γ.

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Section: Lensing In the Schwarzschild-de Sitter Spacetimementioning

confidence: 73%

Section: Lensing In the Mk Spacetime With K =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact gravitational lensing in conformal gravity and Schwarzschild–de Sitter spacetime

Lim

Wang

2017

Phys. Rev. D

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“…However, since the linear potential leads to a non-asymptotically flat geometry one cannot actually use (5.6). Studies that took the asymptotic behavior of the conformal gravity metric given in (7.10) into consideration may be found in [37][38][39][40][41]. The present work provides some additional insight into the issue and its follow up could prove to be instructive.…”

Section: Departures From Geodesic Behavior In the Conformal Gravity Casementioning

confidence: 76%

Critique of the use of geodesics in astrophysics and cosmology

Mannheim¹

2021

Preprint

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Since particles obey wave equations, in general one is not free to postulate that particles move on the geodesics associated with test particles. Rather, for this to be the case one has to be able to derive such behavior starting from the equations of motion that the particles obey, and to do this for either massless or massive particles one can employ the eikonal approximation. While for massive particles one does obtain standard geodesic behavior this way, for a conformally coupled massless scalar field the eikonal approximation only leads to geodesic behavior if the Ricci scalar is zero. Similarly, for the propagation of the light waves associated with the conformal invariant Maxwell equations geodesic behavior only holds if the Ricci tensor is zero. While for practical purposes such terms might only be of relevance in regions of high curvature, the point of this paper is only to establish their presence in principle. Thus in principle the standard null-geodesic-based gravitational bending formula and the behavior of light rays in cosmology are in need of modification in regions with high enough curvature. We show how to appropriately modify the geodesic equations in such situations. We show that relativistic eikonalization has an intrinsic light-front structure, and show that eikonalization in a theory with local conformal symmetry leads to trajectories that are only globally conformally symmetric. The modifications to geodesics that we find lead to the propagation of massless particles off the light cone. This is a curved space reflection of the fact that when light travels through a refractive medium in flat spacetime its velocity is modified from its free flat spacetime value. In the presence of gravity spacetime itself acts as a medium, and this medium can then take light waves off the light cone.

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“…In the context of the brane world scenario, the null geodesics have been considered in [46]- [47]. The geodesic analysis around black holes in Horava-Lifshitz gravity, Einstein-Maxwelldilaton gravity and conformal weyl gravity have been discussed in [48]- [63], respectively. The null geodesics of Born-Infeld black holes have been considered in [64]- [67].…”

Section: Introductionmentioning

confidence: 99%

Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence

Heydari-Fard,

Heydari-Fard

2021

Preprint

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We study the properties of the null geodesics of four-dimensional Einstein-Gauss-Bonnet black holes surrounded by quintessence matter. Due to the quintessence correction, we discuss the radial and non-radial geodesics. For the case of non-radial geodesics we obtain the effective potential, photon sphere and impact parameter associated to the null geodesics in details. We analyze the different possible orbits of massless particles (i.e. photons) such as unstable circular orbits and unbounded orbits and investigate the role of the Gauss-Bonnet coupling α and the quintessence parameter q on the null geodesic trajectories. Moreover, we study the effects of the model parameters on the shadow cast by such black holes. The results are compared to that of Schwarzschild black hole with and without quintessence matter and four-dimensional Einstein-Gauss-Bonnet black holes without quintessence. As a physical application of null geodesics, the deflection angle is calculated and the effect of the quintessence matter on it is investigated.

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Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

Cited by 22 publications

References 59 publications

Exact gravitational lensing in conformal gravity and Schwarzschild–de Sitter spacetime

Exact gravitational lensing in conformal gravity and Schwarzschild–de Sitter spacetime

Critique of the use of geodesics in astrophysics and cosmology

Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence

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