scholarly journals Deflection of light in equatorial plane due to Kerr-Taub-NUT body

2017 ◽  
pp. 23-32
Author(s):  
Sarani Chakraborty ◽  
A.K. Sen
Keyword(s):  
General Relativity ◽  
Equatorial Plane ◽  
Deflection Angle ◽  
Order Term ◽  
Null Geodesic ◽  
Noticeable Effect ◽  
Bending Angle ◽  
Fourth Order Term ◽  
Magnetic Mass ◽  
The Deflection Angle

According to General Relativity, there are factors like mass, rotation, charge and presence of Cosmological constant that can influence the path of light ray. Apart from these factors, many authors have also reported the influence of gravitomagnetism on the path of light ray. In this study we have discussed the effect of a rotating Kerr-Taub-NUT body where the strength of the gravitomagnetic monopole is represented by the NUT factor or magnetic mass. We use the null geodesic of photon method to obtain the deflection angle of light ray for a Kerr-Taub-NUT body in equatorial plane upto the fourth order term. Our study shows that the NUT factor has a noticeable effect on the path of the light ray. By considering the magnetism to be zero, the expression of bending angle gets reduced to the Kerr bending angle. However, we obtained a non-zero bending angle for a hypothetical massless, magnetic body.

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.

The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

scholarly journals Deflection of light by a Coulomb charge in Born–Infeld electrodynamics

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Jin Young Kim
Keyword(s):  
Black Hole ◽  
Electric Field ◽  
Deflection Angle ◽  
Strong Electric Field ◽  
Background Field ◽  
Geodesic Equation ◽  
Bending Angle ◽  
Propagation Of Light ◽  
The Deflection Angle ◽  
Trajectory Equation

AbstractWe study the propagation of light under a strong electric field in Born–Infeld electrodynamics. The nonlinear effect can be described by the effective indices of refraction. Because the effective indices of refraction depend on the background electric field, the path of light can be bent when the background field is non-uniform. We compute the bending angle of light by a Born–Infeld-type Coulomb charge in the weak lensing limit using the trajectory equation based on geometric optics. We also compute the deflection angle of light by the Einstein–Born–Infeld black hole using the geodesic equation and confirm that the contribution of the electric charge to the total bending angle agree.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

scholarly journals Gravitational bending angle with finite distances by Casimir wormholes

2021 ◽  
Author(s):  
Í. D. D. Carvalho ◽  
G. Alencar ◽  
C. R. Muniz
Keyword(s):  
Uncertainty Principle ◽  
Deflection Angle ◽  
Generalized Uncertainty Principle ◽  
Casimir Energy ◽  
Type Ii ◽  
Bending Angle ◽  
Test Particles ◽  
Self Consistent ◽  
The Deflection Angle ◽  
Jacobi Metric

In this paper, we investigate the gravitational bending angle due to the Casimir wormholes, which consider the Casimir energy as the source. Furthermore, some of these Casimir wormholes regard Generalized Uncertainty Principle (GUP) corrections of Casimir energy. We use the Ishihara method for the Jacobi metric, which allows us to study the bending angle of light and massive test particles for finite distances. Beyond the uncorrected Casimir source, we consider many GUP corrections, namely, the Kempf, Mangano and Mann (KMM) model, the Detournay, Gabriel and Spindel (DGS) model, and the so-called type II model for the GUP principle. We also find the deflection angle of light and massive particles in the case of the receiver and the source are far away from the lens. In this case, we also compute the optical scalars: convergence and shear for these Casimir wormholes as a gravitational weak lens. Our self-consistent iterative calculations indicate corrections to the bending angle by Casimir wormholes in the previous paper.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

Relativity and View Effects

2021 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

scholarly journals Relativity and View Effects

2021 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

scholarly journals Relativity and View Effects

2020 ◽  
Author(s):  
Bernard Fischli
Keyword(s):  
General Relativity ◽  
Deflection Angle ◽  
Point Of View ◽  
Speed Limit ◽  
Implicit Assumption ◽  
Energy Exchanges ◽  
Newton’S Laws ◽  
The Deflection Angle ◽  
New Interpretation ◽  
Relativistic View

Abstract Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity.

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