scholarly journals Comparison of vacuum static quadrupolar metrics

2018 ◽  
Vol 5 (5) ◽  
pp. 170826 ◽  
Author(s):  
Francisco Frutos-Alfaro ◽  
Hernando Quevedo ◽  
Pedro A. Sanchez
Keyword(s):  
Symmetric Solution ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Schwarzschild Metric ◽  
Asymptotic Flatness ◽  
Spherically Symmetric Solution ◽  
Vacuum Solutions

We investigate the properties of static and axisymmetric vacuum solutions of Einstein equations which generalize the Schwarzschild spherically symmetric solution to include a quadrupole parameter. We test all the solutions with respect to elementary and asymptotic flatness and curvature regularity. Analysing their multipole structure, according to the relativistic invariant Geroch definition, we show that all of them are equivalent up to the level of the quadrupole. We conclude that the q -metric, a variant of the Zipoy–Voorhees metric, is the simplest generalization of the Schwarzschild metric, containing a quadrupole parameter.

scholarly journals A Spherically Symmetric Solution of \(R+\lambda R^2\) Gravity

2014 ◽  
Vol 24 (3S2) ◽  
pp. 23-28
Author(s):  
Bui Quyet Thang ◽  
Do Thi Huong
Keyword(s):  
Symmetric Solution ◽  
Empty Space ◽  
Spherically Symmetric ◽  
Schwarzschild Solution ◽  
Einstein Theory ◽  
Schwarzschild Metric ◽  
Spherically Symmetric Solution

We shortly review the metric formalism for the \(f(R)\)  gravity.  Based on the metric formalism, westudy the spherically symmetric static empty space solutions with the gravity Lagrangian\(L=R+\lambda R^2\). We found the general metric that described the static empty space with thespherically symmetry.  Our result is more general than Schwarzschild  solution, specially thepredicted metric is perturbed Schwarzschild metric of the Einstein theory.

Experimental tests of a new theory of gravitation

1981 ◽  
Vol 59 (2) ◽  
pp. 283-288 ◽  
Author(s):  
J. W. Moffat
Keyword(s):  
Upper Bound ◽  
Symmetric Solution ◽  
Satellite Orbit ◽  
Experimental Tests ◽  
Spherically Symmetric ◽  
The Sun ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Perihelion Shift ◽  
Theory Of Gravitation

The predictions for the perihelion shift, the deflection of light, and the delay time of a light ray are calculated in the nonsymmetric theory of gravitation. An upper bound for the parameter l (that occurs as a constant of integration in the static, spherically symmetric solution of the field equations) is obtained for the sun for the experimental value of the perihelion shift of Mercury, yielding [Formula: see text]. The upper bound on [Formula: see text] obtained from the Viking spacecraft time-delay experiment is [Formula: see text]. For [Formula: see text], we find that the theory is consistent with the standard relativistic experiments for the solar system. The theory predicts that the perihelion of a satellite could reverse its direction of precession if it orbits close enough to the sun. The results for a highly eccentric satellite orbit are calculated in terms of the value [Formula: see text].

scholarly journals Testing Generalized Einstein-Cartan-Kibble-Sciama Gravity Using Weak Deflection Angle and Shadow Cast

2020 ◽  
Author(s):  
Ali Övgün ◽  
İzzet Sakallı
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Symmetric Solution ◽  
Deflection Angle ◽  
Spherically Symmetric ◽  
Plasma Medium ◽  
Asymptotically Flat ◽  
Spherically Symmetric Solution ◽  
Shadow Cast ◽  
Bonnet Theorem

In this paper, we use a new asymptotically flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity to study the weak gravitational lensing and its shadow cast. To this end, we first compute the weak deflection angle of generalized ECKS black hole using the Gauss–Bonnet theorem in plasma medium and in vacuum. Next by using the Newman-Janis algorithm without complexification, we derive the rotating generalized ECKS black hole and in the sequel study its shadow. Then, we discuss the effect of the ECKS parameter on the shadow of the black hole and weak deflection angle. In short, the goal of this paper is to give contribution to the ECKS theory and look for evidences to understand how the ECKS parameter effects the gravitational lensing.

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