Combining Cauchy and characteristic codes. IV. The characteristic field equations in axial symmetry

1997 ◽  
Vol 56 (2) ◽  
pp. 772-784 ◽  
Author(s):  
Ray A. d’Inverno ◽  
James A. Vickers
Keyword(s):  
Axial Symmetry ◽  
Field Equations ◽  
Characteristic Field

EXACT SOLUTIONS FOR SELF-DUAL SU(2) GAUGE THEORY WITH AXIAL SYMMETRY

2001 ◽  
Vol 16 (11) ◽  
pp. 685-692 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
C. BANDAC
Keyword(s):  
Gauge Theory ◽  
Axial Symmetry ◽  
Dimensional Space ◽  
Space Time ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Invariant ◽  
Local Gauge ◽  
Dimensional Space Time ◽  
Strength Tensor

A model of SU(2) gauge theory is constructed in terms of local gauge-invariant variables defined over a four-dimensional space–time endowed with axial symmetry. A metric tensor gμν is defined starting with the components [Formula: see text] of the strength tensor and its dual [Formula: see text]. The components gμν are interpreted as new local gauge-invariant variables. Imposing the condition that the new metric coincides with the initial metric we obtain the field equations for the considered ansatz. We obtain the same field equations using the condition of self-duality. It is concluded that the self-dual variables are compatible with the axial symmetry of the space–time. A family of analytical solutions of the gauge field equations is also obtained. The solutions have the confining properties. All the calculations are performed using the GRTensorII computer algebra package, running on the MapleV platform.

scholarly journals Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

1932 ◽  
Vol 3 (1) ◽  
pp. 37-45 ◽  
Author(s):  
J. D. Parsons
Keyword(s):  
Field Theory ◽  
General Solution ◽  
Axial Symmetry ◽  
Unified Field Theory ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Unified Field ◽  
Theory Of Gravitation

In a recent paper Dr G. C. McVittie discussed the solution with axial symmetry of Einstein's new field-equations in his Unified Field Theory of Gravitation and Electricity. Owing to an error in his calculation of the field equations, Dr McVittie did not obtain the general solution, which we discuss in the present paper.

A Method for Numerical Integration of Time-Dependent Einstein Equations

1973 ◽  
Vol 51 (7) ◽  
pp. 743-750 ◽  
Author(s):  
J. Pachner ◽  
R. Teshima
Keyword(s):  
Initial Data ◽  
Numerical Integration ◽  
Numerical Computation ◽  
Axial Symmetry ◽  
Einstein Equations ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Field Equations

A method for the numerical computation of the initial data and for the numerical integration of the exact Einstein field equations is described for the case of a rotating incoherent matter with axial symmetry. The results of the integration show that the method gives reliable results.

scholarly journals Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

1931 ◽  
Vol 2 (3) ◽  
pp. 140-150 ◽  
Author(s):  
G. C. McVittie
Keyword(s):  
Field Theory ◽  
Axial Symmetry ◽  
Spherical Symmetry ◽  
Unified Field Theory ◽  
Field Equations ◽  
Mass Particle ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
Axis Of Symmetry ◽  
Single Coordinate

Einstein has recently adopted a new set of field-equations in his Unified Field-Theory of Gravitation and Electricity, the so-called theory of parallelism at a distance or Teleparallelism, and has given a solution of these equations with spherical symmetry, corresponding to the field of a charged mass-particle. In the present paper we discuss the solution of these equations with axial symmetry, which corresponds to a statical field whose field-variables depend on a single coordinate only, viz. the coordinate which is measured along the axis of symmetry.

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