scholarly journals Determining the Topology and Deflection Angle of Ringholes via Gauss-Bonnet Theorem

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 44
Author(s):  
Kimet Jusufi
Keyword(s):  
Deflection Angle ◽  
Characteristic Number ◽  
Weak Limit ◽  
Surface Topology ◽  
Throat Radius ◽  
Wormhole Throat ◽  
Special Cases ◽  
Gravitational Deflection Of Light ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this letter, we use a recent wormhole metric known as a ringhole [Gonzalez-Diaz, Phys. Rev. D 54, 6122, 1996] to determine the surface topology and the deflection angle of light in the weak limit approximation using the Gauss-Bonnet theorem (GBT). We apply the GBT and show that the surface topology at the wormhole throat is indeed a torus by computing the Euler characteristic number. As a special case of the ringhole solution, one can find the Ellis wormhole which has the surface topology of a 2-sphere at the wormhole throat. The most interesting results of this paper concerns the problem of gravitational deflection of light in the spacetime of a ringhole geometry by applying the GBT to the optical ringhole geometry. It is shown that, the deflection angle of light depends entirely on the geometric structure of the ringhole geometry encoded by the parameters b0 and a, being the ringhole throat radius and the radius of the circumference generated by the circular axis of the torus, respectively. As special cases of our general result, the deflection angle by Ellis wormhole is obtained. Finally, we work out the problem of deflection of relativistic massive particles and show that the deflection angle remains unaltered by the speed of the particles.

scholarly journals Deflection angle of light by wormholes using the Gauss–Bonnet theorem

2017 ◽  
Vol 14 (12) ◽  
pp. 1750179 ◽  
Author(s):  
Kimet Jusufi
Keyword(s):  
Deflection Angle ◽  
Weak Limit ◽  
Space Time ◽  
Geometrical Method ◽  
Optical Geometry ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Limit Approximation

In this paper, we have investigated the deflection angle of light by wormholes using a new geometrical method known as Gibbons–Werner method (GW). In particular, we have calculated the deflection angle of light in the weak limit approximation in two wormhole space–time geometries: Ellis wormhole and Janis–Newman–Winnicour (JNW) wormhole. We have employed the famous Gauss–Bonnet theorem (GBT) to the Ellis wormhole optical geometry and JNW wormhole optical geometry, respectively. By using GBT, we computed the deflection angles in leading orders by these wormholes and our results were compared with the ones in the literature.

scholarly journals Weak Deflection Angle by Casimir Wormhole Using Gauss-Bonnet Theorem and Its Shadow

2020 ◽  
Author(s):  
Wajiha Javed ◽  
Ali Hamza ◽  
Ali Övgün
Keyword(s):  
Event Horizon ◽  
Deflection Angle ◽  
Weak Limit ◽  
Plasma Medium ◽  
Spacetime Geometry ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Limit Approximation ◽  
Optical Metric

Here we calculate the deflection angle of photon by Casimir wormhole in weak limit approximation. First we calculate Gaussian optical curvature with the help of optical spacetime geometry and so we use the Gauss-Bonnet theorem on Gaussian optical metric and find deflection angle of photon by Casimir wormhole. Moreover, we calculate the photon's deflection angle in the presence of plasma medium and we also see the graphical nature of deflection angle in both cases. After calculating the deflection angle of Casimir wormhole. Now, we move towards the shadow of Casimir wormhole. After the observations of Event Horizon Telescope, the study of shadow become very important so that we plot the shapes of shadow of Casimir wormhole, and we calculate the photon geodesic around the Casimir wormhole.

scholarly journals Effect of Non-Linear Electrodynamics on Weak Field Deflection Angle by Black Hole

2020 ◽  
Author(s):  
Wajiha Javed ◽  
Ali Hamza ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Weak Limit ◽  
Spacetime Geometry ◽  
Weak Gravitational Field ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this work, we investigate the weak deflection angle of light from exact black hole within the non-linear electrodynamics. First we calculate the Gaussian optical curvature using the optical spacetime geometry. With the help of modern geometrical way popularized by Gibbons and Werner, we examine the deflection angle of light from exact black hole. For this desire, we determine the optical Gaussian curvature and execute the Gauss-Bonnet theorem on optical metric and calculate the leading terms of deflection angle in the weak limit approximation. Furthermore, we likewise study the plasma medium's effect on weak gravitational lensing by exact black hole. Hence we expose the effect of the non-linear electrodynamics on the deflection angle in the weak gravitational field.

scholarly journals Deflection Angle of Photon from Magnetized Black Hole and Effect of Nonlinear Electrodynamics

2019 ◽  
Author(s):  
Wajiha Javed ◽  
jameela Abbas ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Weak Limit ◽  
Nonlinear Electrodynamics ◽  
Leading Order ◽  
Hole Charge ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Limit Approximation ◽  
Optical Metric

In this paper, we proposed a new model of non-linear electrodynamics with parameter. Firstly, we study the weak limit approximation and by using the Gauss Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole and effect of bnon-linear electrodynamics. In doing so, we find the corresponding optical metric after that we calculate the Gaussian curvature which is used in Gauss Bonnet theorem. Then we show the deflection angle in the leading order terms. We also analyzed that our results reduces into Maxwell's electrodynamics and RN solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

scholarly journals Light deflection by a quantum improved Kerr black hole pierced by a cosmic string

2019 ◽  
Vol 16 (08) ◽  
pp. 1950116 ◽  
Author(s):  
Kimet Jusufi ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Cosmic String ◽  
Quantum Correction ◽  
Deflection Angle ◽  
Kerr Black Hole ◽  
Weak Limit ◽  
Global Topology ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Limit Approximation

In this work, we calculate the quantum correction effects on the deflection of light in the space-time geometry of a quantum improved Kerr black hole pierced by an infinitely long cosmic string. More precisely, we calculate the deflection angle by applying the Gauss–Bonnet theorem (GBT) to the osculating optical geometries related to the quantum improved rotating black hole in the weak limit approximation. We find that the deflection angle of light is affected by the quantum effects as well as the global topology due to the presence of the cosmic string. Besides, we have managed to find the same expression for the deflection angle in leading order terms using the geodesic equations.

scholarly journals Quantum effects on the deflection of light and the Gauss–Bonnet theorem

2017 ◽  
Vol 14 (10) ◽  
pp. 1750137 ◽  
Author(s):  
Kimet Jusufi
Keyword(s):  
Deflection Angle ◽  
Weak Limit ◽  
Quantum Corrections ◽  
Leading Order ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Solution ◽  
Bohmian Quantum Mechanics ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Limit Approximation

In this paper, we apply the Gauss–Bonnet (GB) theorem to calculate the deflection angle by a quantum-corrected Schwarzschild black hole in the weak limit approximation. In particular, we calculate the light deflection by two types of quantum-corrected black holes: the renormalization group improved Schwarzschild solution and the quantum-corrected Schwarzschild solution in Bohmian quantum mechanics. We start from the corresponding optical metrics to use then the GB theorem and calculate the Gaussian curvature in both cases. We calculate the leading terms of the deflection angle and show that quantum corrections modify the deflection angle in both solutions. Finally by performing geodesics calculations we show that GB method gives exact results in leading-order terms.

scholarly journals Effect of Aether Field on Weak Deflection Angle of Black Holes

2019 ◽  
Author(s):  
Ali Övgün ◽  
İzzet Sakallı ◽  
Joel Saavedra
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Limit ◽  
Spherically Symmetric ◽  
Light Rays ◽  
Topological Effect ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Limit Approximation

We study the light rays in a static and spherically symmetric gravitational field of null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations show how gravitational lensing is affected by the NAT field. We also show once again that the bending of light stems from a global and topological effect.

scholarly journals Weak Deflection Angle of some Classes of non-linear Electrodynamics Black Holes via Gauss-Bonnet Theorem

2020 ◽  
Author(s):  
Hasan El Moumni ◽  
Karima Masmar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Leading Order ◽  
Plasma Medium ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

scholarly journals Effect of Horndeski Theory on Weak Deflection Angle Using the Gauss-Bonnet Theorem

2021 ◽  
Author(s):  
Ali Övgün ◽  
Yashmitha Kumaran ◽  
Wajiha Javed ◽  
Jameela Abbas
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Field Approximation ◽  
Weak Field ◽  
Plasma Medium ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
The Impact ◽  
Do So

The main goal of this paper is to study the weak gravitational lensing by Horndeski black hole in weak field approximation. In order to do so, we exploit the Gibbons-Werner method to the optical geometry of Horndeski black hole and implement the Gauss-Bonnet theorem to accomplish the deflection angle of light in weak field region. Furthermore, we have endeavored to extend the scale of our work by comprising the impact of plasma medium on the deflection angle as properly. Later, the graphical influence of the deflection angle of photon on Horndeski black hole in plasma and non-plasma medium is examined.

scholarly journals The Effect of the Brane-Dicke Coupling Parameter on Weak Gravitational Lensing by  Wormholes and Naked Singularities

2019 ◽  
Author(s):  
Wajiha Javed ◽  
Rimsha Babar ◽  
Ali Övgün
Keyword(s):  
Gravitational Lensing ◽  
Deflection Angle ◽  
Coupling Parameter ◽  
Weak Field ◽  
Anisotropic Pressure ◽  
Naked Singularities ◽  
Weak Field Limit ◽  
The Deflection Angle ◽  
Geometric Techniques ◽  
Bonnet Theorem

In this paper, we analyze the deflection angle of light by Brane-Dicke wormhole in the weak field limit approximation to find the effect of the Brane-Dicke coupling parameter on the weak gravitation lensing. For this purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and optical geometry in order to calculate the deflection angle. Furthermore, we verify our results by considering the most familiar geodesic technique. Moreover, we establish the quantum corrected metric of Brane-Dicke wormhole by replacing the classical geodesic with Bohmian trajectories, whose matter source and anisotropic pressure are influenced by Bohmian quantum effects and calculate its quantum corrected deflection angle. Then, we calculate the deflection angle by naked singularities and compare with the result of wormhole's. Such a novel lensing feature might serve as a way to detect wormholes, naked singularities and also the evidence of Brane-Dicke theory.

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