SOME ASPECTS OF EXACT STATIC SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN’S FIELD EQUATIONS WITH SPECIFIED EQUATION OF STATE

2020 ◽  
Vol 9 (11) ◽  
pp. 9097-9108
Author(s):  
A. K. Singh
Keyword(s):  
Equation Of State ◽  
Symmetric Solution ◽  
Spherically Symmetric ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Spherically Symmetric Solution

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].

Black holes

2019 ◽  
pp. 80-91
Author(s):  
Steven Carlip
Keyword(s):  
Black Hole ◽  
Solar System ◽  
Symmetric Solution ◽  
Vacuum Solution ◽  
Interior Solution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Killing Horizon ◽  
Spherically Symmetric Solution ◽  
Trapped Surface

Chapter 3 used the Schwarzschild metric to obtain predictions for the Solar System. In this chapter, that metric is derived as the unique static, spherically symmetric solution of the vacuum Einstein field equations. For the Solar System, this vacuum solution must be joined to an “interior solution” describing the interior of the Sun. Such solutions are discussed briefly. If, on the other hand, one assumes “vacuum all the way down,” the solution describes a black hole. The chapter analyzes the geometry and physics of the nonrotating black hole: the event horizon, the Kruskal-Szekeres extension, the horizon as a trapped surface and as a Killing horizon. Penrose diagrams are introduced, and a short discussion is given of the four laws of black hole mechanics.

scholarly journals Spherically Symmetric Solution in (1+4)-Dimensionalf(T)Gravity Theories

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Symmetric Solution ◽  
Vacuum Solution ◽  
Azimuthal Angle ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
The Third ◽  
Special Vacuum ◽  
Spherically Symmetric Solution

A nondiagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinaterplus an angleΦ, which is a generalization of the azimuthal angleϕ, is applied to the field equations of (1+4)-dimensionalf(T)gravity theory. A special vacuum solution with one constant of integration is derived. The physical meaning of this constant is shown to be related to the gravitational mass of the system and the associated metric represents Schwarzschild in (1+4)-dimension. The scalar torsion related to this solution vanishes. We put the derived solution in a matrix form and rewrite it as a product of three matrices: the first represents a rotation while the second represents an inertia and the third matrix is the diagonal square root of Schwarzschild spacetime in (1+4)-dimension.

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