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Abstract
Using a new geometrical method introduced by Werner, we find the deflection angle in the weak limit approximation by a spinning cosmic string in the context of the Einstein-Cartan (EC) theory of gravity. We begin by adopting the String-Randers optical metric, then we apply the Gauss-Bonnet theorem to the optical geometry and derive the leading terms of the deflection angle in the equatorial plane. Calculations shows that light deflection is affected by the intrinsic spin of the cosmic string and torsion.
Highlights
Gravitational bending of light by a massive object is a wellknown phenomenon, which led to the first experimental evidence of the general theory of relativity [1]
In the last few years, there has been a growing interest in studying weak as well as strong fields, and along this line of research many papers have been written, addressing for instance the naked singularities and relativistic images of Schwarzschild black hole lensing, the role of the scalar field in gravitational lensing [8–10], wormholes [11], testing the cosmic censorship hypothesis [12], gravitational lensing from charged black holes in the weak field limit [13], Kerr black hole lensing [14], gravitational lensing by massless braneworld black holes [15], and strong deflection lensing by charged black holes in scalar-tensor gravity [16]
From Eq (33), it is clear that the effects of the intrinsic spin and torsion on the light deflection are negligible compared with the deflection angle of the static cosmic string
Summary
Gravitational bending of light by a massive object is a wellknown phenomenon, which led to the first experimental evidence of the general theory of relativity [1]. Even today, the deflection of light continues to be one of the most important tools used in modern astrophysics and cosmology. This phenomenon has been studied in detail in various astrophysical aspects, both in the weak limit [2,3] and the strong limit approximation [4–7]. Like dislocations, appear within Einstein–Cartan gravitation theory [32] in Riemann–Cartan geometry. [36] torsion as an alternative to cosmic inflation is investigated In this context, it is natural to see if torsion affects the light deflection by a spinning cosmic string. 3, we calculate the corresponding Gaussian optical curvature for a spinning cosmic string and using the Gauss–Bonnet theorem, we calculate the leading terms of the deflection angle in the weak limit approximation.
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