scholarly journals Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

2015 ◽  
Vol 24 (02) ◽  
pp. 1530006 ◽  
Author(s):  
Christian Heinicke ◽  
Friedrich W. Hehl
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Symmetric Solution ◽  
Gravitational Theory ◽  
Vacuum Field ◽  
Kerr Solution ◽  
Spherically Symmetric ◽  
Axially Symmetric ◽  
Schwarzschild Solution ◽  
Spherically Symmetric Solution

Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(–Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

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.

SCHWARZSCHILD SOLUTION IN ASHTEKAR FORMALISM

1991 ◽  
Vol 06 (16) ◽  
pp. 1437-1442
Author(s):  
TAKESHI FUKUYAMA ◽  
KIYOSHI KAMIMURA
Keyword(s):  
Gauge Field ◽  
Large Distance ◽  
Symmetric Solution ◽  
Einstein Gravity ◽  
Spherically Symmetric ◽  
Similar Form ◽  
Schwarzschild Solution ◽  
Spherically Symmetric Solution ◽  
Monopole Solution

Spherically symmetric solution of Einstein gravity is studied in the framework of Ashtekar formalism. Schwarzschild solution takes a similar form to the 't Hooft–Polyakov monopole solution. In the former, the gauge field behaves as r−2 at large distance in contrast to r−1 in the latter.

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].

The static spherically symmetric solutions in a unified field theory

1957 ◽  
Vol 53 (2) ◽  
pp. 489-493 ◽  
Author(s):  
John Moffat
Keyword(s):  
Charged Particle ◽  
Electric Energy ◽  
Gravitational Theory ◽  
Spherically Symmetric ◽  
Unified Field Theory ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Fundamental Properties ◽  
Unified Field ◽  
Conditions At Infinity

ABSTRACTA brief account is given of the fundamental properties of a new generalization ((1), (2)) of Einstein's gravitational theory. The field equations are then solved exactly for the case of a static spherically symmetric gravitational and electric field due to a charged particle at rest at the origin of the space-time coordinates. This solution provides information about the gravitational field produced by the electric energy surrounding a charged particle and yields the Coulomb potential field. The solution satisfies the required boundary conditions at infinity, and it reduces to the Schwarzschild solution of general relativity when the charge is zero.

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