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 Approximate perfect fluid solutions with quadrupole moment

2021 ◽  
Author(s):  
Medeu Abishev ◽  
Nurzada Beissen ◽  
Farida Belissarova ◽  
Kuantay Boshkayev ◽  
Aizhan Mansurova ◽  
...  
Keyword(s):  
Perfect Fluid ◽  
Quadrupole Moment ◽  
Line Element ◽  
Approximate Solutions ◽  
Axially Symmetric ◽  
Field Equations ◽  
Matching Conditions ◽  
Fluid Source ◽  
Gravitational Fields ◽  
Spherically Symmetry

We investigate the interior Einstein’s equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational fields. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding line element and field equations and find several classes of vacuum and perfect fluid solutions. We find some particular approximate solutions by imposing appropriate matching conditions.

scholarly journals Evidence of cosmic strings by the observation of the alignment of quasar polarization axes on Mpc scale

2018 ◽  
Vol 27 (09) ◽  
pp. 1850094 ◽  
Author(s):  
Reinoud Jan Slagter
Keyword(s):  
Symmetry Breaking ◽  
Gauge Field ◽  
Cosmic String ◽  
Axial Symmetry ◽  
Approximation Scheme ◽  
Azimuthal Angle ◽  
Goldstone Boson ◽  
Second Order ◽  
Compact Objects ◽  
Warp Factor

The recently found alignment of the polarization axes (PA) of quasars in large quasar groups (LQGs) on Mpc scales can be explained by general relativistic cosmic string networks. By considering the cosmic string as a result of spontaneous symmetry breaking of the gauged U(1) abelian Higgs model with topological charge [Formula: see text], many stability features of [Formula: see text]-vortex solutions of superconductivity can be taken over. Decay of the high multiplicity ([Formula: see text]) super-conducting vortex into a lattice of [Formula: see text] vortices of unit magnetic flux is energetically favorable. The temporarily broken axial symmetry will leave an imprint of a preferred azimuthal-angle on the lattice. The stability of the lattice depends critically on the parameters of the model, especially when gravity comes into play. In order to handle the strong nonlinear behavior of the time-dependent coupled field equations of gravity and the scalar-gauge field, we will use a high-frequency approximation scheme to second order on a warped 5D axially symmetric spacetime with the scalar-gauge field residing on the brane. We consider different winding numbers for the subsequent orders of perturbations of the scalar field. A profound contribution to the energy–momentum tensor comes from the bulk spacetime and can be understood as “dark”-energy. The cosmic string becomes super-massive by the contribution of the 5D Weyl tensor on the brane and the stored azimuthal preferences will not fade away. During the recovery to axial symmetry, gravitational and electro-magnetic radiation will be released. The perturbative appearance of a nonzero energy–momentum component [Formula: see text] can be compared with the phenomenon of bifurcation along the Maclaurin–Jacobi sequence of equilibrium ellipsoids of self-gravitating compact objects, signaling the onset of secular instabilities. There is a kind of similarity with the Goldstone-boson modes of spontaneously broken symmetries of continuous groups. The recovery of the SO(2) symmetry from the equatorial eccentricity takes place on a time-scale comparable with the emission of gravitational waves. The emergent azimuthal-angle dependency in our model can be used to explain the aligned PA in LQGs on Mpc scales. Spin axis direction perpendicular to the major axes of LQGs when the richness decreases can be explained as a second-order effect in our approximation scheme by the higher multiplicity terms. The preferred directions are modulo [Formula: see text], with [Formula: see text] being an integer dependent on the [Formula: see text]th order of approximation. When more data of quasars of high redshift becomes available, one could prove that the alignment emerged after the symmetry breaking scale and must have a cosmological origin. The effect of the warp factor on the second-order perturbations could also be an indication of the existence of extra large dimensions.

Analytic solution of gauge field equations for Lorentz gravity

1989 ◽  
Vol 28 (11) ◽  
pp. 1437-1441
Author(s):  
Wei Mozhen ◽  
Shao Changgui ◽  
He Changbai
Keyword(s):  
Gauge Field ◽  
Analytic Solution ◽  
Field Equations

scholarly journals SECOND ORDER FORMALISM IN POINCARÉ GAUGE THEORY

2007 ◽  
Vol 16 (04) ◽  
pp. 655-679 ◽  
Author(s):  
M. LECLERC
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Type Equation ◽  
Approximate Solutions ◽  
Higher Order ◽  
Second Order ◽  
Field Equations ◽  
Tetrad Field ◽  
Yang Mills ◽  
Source Current

Changing the set of independent variables of Poincaré gauge theory and considering, in a manner similar to the second-order formalism of general relativity, the Riemannian part of the Lorentz connection as a function of the tetrad field, we construct theories that do not contain second or higher order derivatives in the field variables, possess a full general relativity limit in the absence of spinning matter fields, and allow for propagating torsion fields in the general case, the spin density playing the role of the source current in a Yang–Mills type equation for the torsion. The equivalence of the second-order and conventional first-order formalism is established and the corresponding Noether identities are discussed. Finally, a concrete Lagrangian is constructed and by means of a Yasskin-type ansatz, the field equations are reduced to a conventional Einstein–Proca system. Neglecting higher order terms in the spin-tensor, approximate solutions describing the exterior of a spin-polarized neutron star are presented and the possibility of the experimental detection of the torsion fields is briefly discussed.

scholarly journals Post-Newtonian limit: second-order Jefimenko equations

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
David Pérez Carlos ◽  
Augusto Espinoza ◽  
Andrew Chubykalo
Keyword(s):  
Linear Equations ◽  
Space Time ◽  
Second Order ◽  
Field Equations ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Gravity Probe ◽  
Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

scholarly journals A new variation for the relativistic Euler equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mahmoud A. E. Abdelrahman ◽  
Hanan A. Alkhidhr
Keyword(s):  
Euler Equations ◽  
Nonlinear Waves ◽  
Approximation Scheme ◽  
Strength Function ◽  
Convergent Sequence ◽  
Approximate Solutions ◽  
Large Initial Data ◽  
Initial Value ◽  
Relativistic Euler Equations ◽  
Glimm Scheme

Abstract The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

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