Axially symmetric solution to Rosen's field equations with angular momentum

1988 ◽  
Vol 27 (2) ◽  
pp. 283-288 ◽  
Author(s):  
R. J. Knill ◽  
W. R. Stoeger ◽  
A. P. Whitman
Keyword(s):  
Angular Momentum ◽  
Symmetric Solution ◽  
Axially Symmetric ◽  
Field Equations

APPROXIMATE SOLUTIONS OF STATIONARY GAUGE STRINGS ON THE (r, z)-PLANE

1995 ◽  
Vol 04 (02) ◽  
pp. 267-277 ◽  
Author(s):  
R.J. SLAGTER
Keyword(s):  
Angular Momentum ◽  
Gauge Field ◽  
Approximation Scheme ◽  
Analytic Solution ◽  
Approximate Solutions ◽  
Second Order ◽  
Singular Behavior ◽  
Axially Symmetric ◽  
Field Equations ◽  
Symmetric Spacetime

We derive a class of approximate solutions of the coupled Einstein-scalar-gauge field equations on an axially symmetric spacetime. An analytic solution of the resulting elliptic PDE’s can be obtained to any desired order by constructing the Riemann functions. As an example model, a solution is presented, which resembles the Nielsen-Olesen vortex close to the z=0 hyperplane. However, the solution shows some significant deviation from the classical vortex off the z=0 plane. The singular behavior, which one usually encounters in line-mass models, manifests itself through the second-order solutions in the approximation scheme. Further, in this “toy”-model, with sufficient angular momentum of the spinning string, gφφ becomes negative for some values of r.

scholarly journals CHARGED AXIALLY SYMMETRIC SOLUTION, ENERGY AND ANGULAR MOMENTUM IN TETRAD THEORY OF GRAVITATION

2006 ◽  
Vol 21 (15) ◽  
pp. 3181-3197 ◽  
Author(s):  
GAMAL G. L. NASHED
Keyword(s):  
Angular Momentum ◽  
Symmetric Solution ◽  
Vector Fields ◽  
Momentum Density ◽  
Relativity Theory ◽  
Axially Symmetric ◽  
Theory Of Gravitation ◽  
Charge Parameter ◽  
Momentum Complex ◽  
Tetrad Theory

Charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation is derived. The metric associated with this solution is an axially symmetric metric which is characterized by three parameters "the gravitational mass M, the charge parameter Q and the rotation parameter a." The parallel vector fields and the electromagnetic vector potential are axially symmetric. We calculate the total exterior energy. The energy–momentum complex given by Møller in the framework of the Weitzenböck geometry "characterized by vanishing the curvature tensor constructed from the connection of this geometry" has been used. This energy–momentum complex is considered as a better definition for calculation of energy and momentum than those of general relativity theory. The energy contained in a sphere is found to be consistent with pervious results which is shared by its interior and exterior. Switching off the charge parameter, one finds that no energy is shared by the exterior of the charged axially symmetric solution. The components of the momentum density are also calculated and used to evaluate the angular momentum distribution. We found no angular momentum contributes to the exterior of the charged axially symmetric solution if zero charge parameter is used.

scholarly journals Exact Axially Symmetric Solution inf(T)Gravity Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Vacuum Solution ◽  
Gravity Theory ◽  
Kerr Metric ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Kerr Spacetime ◽  
Euler’S Angles

A general tetrad field with sixteen unknown functions is applied to the field equations off(T)gravity theory. An analytic vacuum solution is derived with two constants of integration and an angleΦthat depends on the angle coordinateϕand radial coordinater. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.

Angular momentum in general relativity I. Definition and asymptotic behaviour

1977 ◽  
Vol 354 (1679) ◽  
pp. 379-405 ◽  
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Angular Momentum ◽  
Asymptotic Behaviour ◽  
Event Horizon ◽  
Conservation Law ◽  
General Definition ◽  
Field Equations ◽  
Spin Coefficient ◽  
Coefficient Formalism

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptoticallyflat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.

scholarly journals Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Debojit Sarma ◽  
Faizuddin Ahmed ◽  
Mahadev Patgiri
Keyword(s):  
Naked Singularity ◽  
Empty Space ◽  
Space Time ◽  
Axially Symmetric ◽  
Field Equations ◽  
Closed Timelike Curves ◽  
Asymptotically Flat ◽  
Type D ◽  
Initial Hypersurface ◽  
Petrov Classification

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The space-time is regular everywhere except on the symmetry axis where it possesses a true curvature singularity. The space-time is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the space-time also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.

scholarly journals Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Gravitational Lensing ◽  
Cosmic Time ◽  
Naked Singularity ◽  
Space Time ◽  
Axially Symmetric ◽  
Time Machine ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Closed Orbits ◽  
Group A

We present a gravitational collapse null dust solution of the Einstein field equations. The space-time is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity and admits one parameter isometry group, a generator of axial symmetry along the cylinder which has closed orbits. The space-time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine. The radial geodesics near the singularity and the gravitational lensing (GL) will be discussed. The physical interpretation of this solution, based on the study of the equation of the geodesic deviation, will be presented. It was demonstrated that this solution depends on the local gravitational field consisting of two components with amplitudes Ψ2 and Ψ4.

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