scholarly journals The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Zonghai Li ◽  
Junji Jia
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Kerr Black Hole ◽  
Relativistic Velocity ◽  
Massive Particles ◽  
Finite Distance ◽  
The Deflection Angle ◽  
Jacobi Metric ◽  
Optical Metric ◽  
Gravitational Deflection

Abstract In this paper, we study the weak gravitational deflection of relativistic massive particles for a receiver and source at finite distance from the lens in stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we extend the generalized optical metric method to the generalized Jacobi metric method by using the Jacobi–Maupertuis Randers–Finsler metric. More specifically, we apply the Gauss–Bonnet theorem to the generalized Jacobi metric space and then obtain an expression for calculating the deflection angle, which is related to Gaussian curvature of generalized optical metric and geodesic curvature of particles orbit. In particular, the finite-distance correction to the deflection angle of signal with general velocity in the the Kerr black hole and Teo wormhole spacetimes are considered. Our results cover the previous work of the deflection angle of light, as well as the deflection angle of massive particles in the limit for the receiver and source at infinite distance from the lens object. In Kerr black hole spacetime, we compared the effects due to the black hole spin, the finite-distance of source or receiver, and the relativistic velocity in microlensings and lensing by galaxies. It is found in these cases, the effect of black hole spin is usually a few orders larger than that of the finite-distance and relativistic velocity, while the relative size of the latter two could vary according to the particle velocity, source or observer distance and other lensing parameters.

scholarly journals Finite-Distance Gravitational Deflection of Massive Particles by the Kerr-like Black Hole in the Bumblebee Gravity Model

2019 ◽  
Author(s):  
Zonghai Li ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravity Model ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Geodesic Curvature ◽  
Surface Integral ◽  
Massive Particles ◽  
Finite Distance ◽  
The Deflection Angle ◽  
Gravitational Deflection

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. We then consider the finite-distance correction for the deflection angle of massive particles.

scholarly journals Boosted Kerr Black Hole in the Presence of Plasma

Proceedings ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 6
Author(s):  
Carlos A. Benavides-Gallego ◽  
Ahmadjon-Abdujabbarov Abdujabbarov
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Kerr Black Hole ◽  
Galaxy Cluster ◽  
Field Approximation ◽  
Weak Field ◽  
Weak Field Approximation ◽  
The Deflection Angle ◽  
Isothermal Gas ◽  
Uniform Plasma

In this work, we obtain the deflection angle for a boosted Kerr black hole in the weak field approximation using the optics in a curved spacetime developed by J. L. Synge in 1960. We study the behavior of light in the presence of plasma by considering different distributions: uniform plasma, singular isothermal sphere, non-singular isothermal gas sphere, and plasma in a galaxy cluster. We found that the dragging of the inertial system along with the boosted parameter Λ affect the value of the deflection angle. As an application, we studied the magnification for both uniform and singular isothermal distributions.

Strong gravitational lensing by Kerr–Newman-Nut-Quintessence black hole

2021 ◽  
Author(s):  
Niyaz Uddin Molla ◽  
Ujjal Debnath
Keyword(s):  
Black Hole ◽  
Equatorial Plane ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Null Geodesic ◽  
Kerr Black Hole ◽  
Eos Parameter ◽  
Strong Gravitational Lensing ◽  
Spin Parameter ◽  
The Deflection Angle

We investigate the strong gravitational lensing on equatorial plane as well as quasi-equatorial plane by the Kerr–Newman-Nut-Quintessence (KNNQ) black hole (BH) with the equation of state (EoS) parameter of the quintessence [Formula: see text] and the quintessence density [Formula: see text]. Our results show that the strong gravitational lensing in the KNNQ black hole space–time has some distinct behaviors from those in the backgrounds of the four dimension Kerr black hole. Also, we investigate the strong gravitational lensing on equatorial plane as well as quasi-equatorial plane by the KNNQ BH with the effects of Nut charge, spin parameter and quintessence parameter. First, we calculate the null geodesic equations using the Hamilton–Jacobi separation method. Then we investigate the equatorial lensing by KNNQ black hole. We obtain the deflection angle and deflection coefficients in the equatorial plane, which is affected by EoS parameter of the quintessence [Formula: see text], quintessence density [Formula: see text], Nut parameter [Formula: see text], spin parameter [Formula: see text] and quintessence parameter [Formula: see text] [Formula: see text]. Next, we discuss the lens equation and the observables in the equatorial plane. Finally, we investigate gravitational lensing by the KNNQ black hole in the quasi-equatorial plane. In this work, the quintessence density [Formula: see text], the EoS parameter of the quintessence [Formula: see text], Nut parameter [Formula: see text], spin parameter [Formula: see text] and quintessence parameter [Formula: see text] [Formula: see text] have significant effects on the strong gravitational lensing both in equatorial plane as well as quasi-equatorial plane.

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 Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole

2021 ◽  
Author(s):  
Zonghai Li ◽  
Yujie Duan ◽  
Junji Jia
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Massive Particle ◽  
Field Approximation ◽  
Weak Field ◽  
Coupling Constant ◽  
Finite Distance ◽  
The Deflection Angle ◽  
Electrostatic Coupling ◽  
Bonnet Theorem

Abstract Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel four-dimensional charged Einstein-Gauss-Bonnet black hole. We focus on the weak field approximation and consider the deflection angle with finite distance effects. To this end, we use a geometric and topological method, which is to apply the Gauss-Bonnet theorem to the Jacobi space to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution $\delta_g$, a pure electrostatic $\delta_c$ and a gravitational-electrostatic coupling term $\delta_{gc}$. We find that the deflection angle increases(decreases) if the Gauss-Bonnet coupling constant $\alpha$ is negative(positive). Furthermore, the effects of the BH charge, the particle charge-to-mass ratio and the particle velocity on the deflection angle are analyzed.

scholarly journals Bounding Greybody and Deflection Angle of Improved Schwarzschild Black Hole

2021 ◽  
Author(s):  
Wajiha Javed ◽  
Muhammad Aqib ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Graphical Analysis ◽  
Plasma Medium ◽  
Schwarzschild Black Hole ◽  
Weak Gravitational Lensing ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Optical Metric

We explore the deflection angle in the framework of improved Schwarzschild Black hole utilizing the most advance geometrical path adopted by Gibbon-Werner. To investigate deflection angle of the photon ray by weak gravitational lensing for this black hole, we derive the optical curvature and perform the application of Gauss-Bonnet theorem on the optical metric. Moreover, we study the impacts of the plasma medium in context of the weak gravitational lensing in relate to this black hole. Further, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Also, we find the rigorous bound base upon the greybody factor for improved Schwarzschild black hole. A while later, we contrast our conclusions about deflection angle with the deflection angles of Schwarzschild black hole within plasma and non-plasma mediums.

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 SIGNATURES OF TEV SCALE GRAVITY IN HIGH ENERGY COLLISIONS

2005 ◽  
Vol 20 (16) ◽  
pp. 1203-1208 ◽  
Author(s):  
A. NICOLAIDIS ◽  
N. G. SANCHEZ
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Logarithmic Singularity ◽  
High Energy ◽  
Particle Collisions ◽  
High Energy Collisions ◽  
The Deflection Angle ◽  
Impact Parameters ◽  
Matter Fields ◽  
Schwarzschild Radius

In TeV scale unification models, gravity propagates in 4+δ dimensions while gauge and matter fields are confined to a four-dimensional brane, with gravity becoming strong at the TeV scale. For a such scenario, we study strong gravitational interactions in an effective Schwarzschild geometry. Two distinct regimes appear. For large impact parameters, the ratio ρ~(Rs/r0)1+δ, (with Rs the Schwarzschild radius and r0 the closest approach to the black hole), is small and the deflection angle χ is proportional to ρ (this is like Rutherford-type scattering). For small impact parameters, the deflection angle χ develops a logarithmic singularity and becomes infinite for ρ = ρ c = 2/(3+δ). This singularity is reflected into a strong enhancement of the backward scattering (like a glory-type effect). We suggest as distinctive signature of black hole formation in particle collisions at TeV energies, the observation of backward scattering events and their associated diffractive effects.

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