GRAVITATIONAL FIELD OF A STRAIGHT COSMIC STRING IN THE FRAMEWORK OF HIGHER-DERIVATIVE GRAVITY

2008 ◽  
Vol 23 (24) ◽  
pp. 1999-2009 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
JOSÉ HELAYËL-NETO ◽  
MATHEUS LOBO
Keyword(s):  
Gravitational Field ◽  
Cosmic String ◽  
Short Range ◽  
Gravitational Force ◽  
Deflection Angle ◽  
Einstein Gravity ◽  
Nonrelativistic Limit ◽  
Higher Derivative ◽  
The Deflection Angle ◽  
The Impact

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the deflection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.

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 Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Junji Jia ◽  
Ke Huang
Keyword(s):  
Gravitational Lensing ◽  
Deflection Angle ◽  
Strong Field ◽  
Distance Effect ◽  
Critical Value ◽  
Field Limit ◽  
Perturbative Method ◽  
The Deflection Angle ◽  
The Impact ◽  
Strong Field Limit

AbstractA perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $$(1-b_c/b)$$ ( 1 - b c / b ) where b is the impact parameter and $$b_c$$ b c is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter l and the asymptotic velocity v of the signal. The BH shadow size were found to decrease slightly as l increases to its critical value, and increase as v decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of l and decrease of v will increase their values.

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 Miniature Ultralight Deformable Squama Mechanics and Skin Based on Piezoelectric Actuation

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 969
Author(s):  
Xiang Lu ◽  
Xiang Xi ◽  
Kun Lu ◽  
Chengxiang Wang ◽  
Xiang Chen ◽  
...  
Keyword(s):  
Mobile Phone ◽  
Short Range ◽  
Deflection Angle ◽  
Array Processing ◽  
Mechanical Deformation ◽  
Piezoelectric Actuation ◽  
Contact Control ◽  
Piezoelectric Control ◽  
Different Shapes ◽  
The Deflection Angle

A miniature deformable squama mechanics based on piezoelectric actuation inspired by the deformable squama is proposed in this paper. The overall size of the mechanics is 16 mm × 6 mm × 6 mm, the weight is only 140 mg, the deflection angle range of the mechanical deformation is −15°~45°, and the mechanical deformation is controllable. The small-batch array processing of the miniature deformable squama mechanics, based on the stereoscopic process, laid the technological foundation for applying the deformed squama array arrangement. We also designed and manufactured a small actuation control boost circuit and a mobile phone piezoelectric control assistant application that makes it convenient to perform short-range non-contact control of the deformation of the squama. The proposed system arranges the deformed squamae into groups to form the skin and controlls the size and direction of the signals input to each group of the squama array, thereby making the skin able to produce different shapes to create deformable skin.

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 Testing Einstein’s formula for gravitational deflection of light based on lightcurves of microlensed sources

2019 ◽  
pp. 16-20
Author(s):  
A.N. Alexandrov ◽  
V.I. Zhdanov ◽  
V.M. Sliusar
Keyword(s):  
Impact Parameter ◽  
Deflection Angle ◽  
Light Deflection ◽  
Classical Formula ◽  
Deflection Of Light ◽  
Gravitational Deflection Of Light ◽  
The Deflection Angle ◽  
The Impact ◽  
Gravitational Deflection

We propose a new test of the Einstein’s formula for the gravitational light deflection using the Galactic microlensing. In this classical formula, the deflection angle ∆ϕ is inversely proportional to the impact parameter p of incoming photons travelling from infinity.

scholarly journals Numerical simulations for the interaction of the NGC 1333 IRAS 4A outflow and an ambient cloud

2006 ◽  
Vol 2 (S237) ◽  
pp. 392-392
Author(s):  
Chang Hyun Baek ◽  
Jongsoo Kim ◽  
Minho Choi
Keyword(s):  
Deflection Angle ◽  
Initial Conditions ◽  
Density Ratio ◽  
Young Stellar Objects ◽  
Tvd Scheme ◽  
Detailed Model ◽  
Dense Cloud ◽  
The Deflection Angle ◽  
The Impact ◽  
Cloud Core

NGC 1333 contains numerous young stellar objects and outflows and is a well-studied star formation region. High resolution SiO observations of the NGC 1333 IRAS 4A region showed a highly collimated outflow with a substantial deflection angle. It was also suggested by the observations that the deflection was due to the interaction of the outflow and a dense cloud core (Choi 2005a, 2005b). In order to make a detailed model of the deflected outflow, we have carried out three-dimensional hydrodynamic simulations of outflow/cloud interactions with a hydrodynamic code based on the TVD scheme. In our models, an initial outflow with number density 10 cm−3 and temperature 104 K interacts with a spherical cloud with a power-law density distribution. The cloud has a uniform temperature of 10 K and is surrounded by a homogeneous gas of density 100 cm−3 and temperature 10 K. The radius of the cloud is 0.02 pc, and the outflow has a sectional radius 300 AU. Through the numerical experiments, we found that the deflection angle is mainly determined by the impact parameter and the density ratio between the outflow and the impact zone of the cloud. The deflection angle is, however, not sensitive to the velocity of outflow. Using initial conditions and parameters which are particularly suitable for NGC 1333 IRAS 4A, we can reproduce its bent morphology. We therefore confirm that the northeastern deflected outflow of the NGC 1333 IRAS 4A may be colliding with a dense cloud core and deflected as a result.

scholarly journals Weak Gravitational Lensing by Horndeski Theory Using the Gauss-Bonnet Theorem

2020 ◽  
Author(s):  
Wajiha Javed ◽  
Jameela Abbas ◽  
Yashmitha Kumaran ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Field Approximation ◽  
Weak Field ◽  
Plasma Medium ◽  
Weak Gravitational Lensing ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
The Impact

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 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.

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