arXiv subjects

Andri Husein

Publications and source records attributed to Andri Husein.

9 recordsLinked to original sources

arXiv2018

Vortex Solution of a Twisted Baby Skyrme Equation

We examine non-linear sigma (plus Skyrme term) model in flat space, in particular with a twist, which comprises a twisted baby Skyrmion vortex solution with an added dependence on a twist term $mkz$, where $z$ is the vertical coordinate. We find that the solutions should have asymptotic form. We also find that mass per unit length of string, $μ$, increases roughly linearly with $ζ$, where $ζ=4λ^2K_s(mk)^2$, $λ$ is scaling constant, $K_s$ is Skyrme term, $m$ is integer and $k$ is wave number.

hep-th↗

arXiv2018

Non-Twisting and Twisting Solutions of the Einstein Field Equations of a Skyrmionic String

We construct non-linear sigma model plus Skyrme term (Skyrme model) with a twist in the gravitational field. We try to solve the Einstein field equations for small and large values of $r$, with and without twist. We prove that no non-twisting or twisting solutions extending from $r=0$ to $r=\infty$ exist. At last, we try to solve non-twisting and twisting solutions of the Einstein field equations with a finite radius. We find that there are no solutions with a finite radius that can satisfy the junction conditions at the boundary radius $r=r_b$, where $r_b$ is a finite radius.

gr-qc↗

arXiv2018

Topological and Hopf charges of a twisted Skyrmion string

We examine nonlinear sigma models, in particular the Skyrme model with a twist (the twisted Skyrmion string), which comprises a vortex solution with an added dependence on a twist term $mkz$, where $z$ is the vertical coordinate. The topological and Hopf charges of a twisted Skyrmion string are calculated and are shown to be equivalent to the winding number $n$ of the vortex and proportional to $nmk$, respectively. The principle of conservation of the Hopf charge, which is a standard property of the baby Skyrmion model, is generalised to cover the non-compact twisting solutions studied here.

hep-th↗

arXiv2018

Vortex Solution of the Gravitational Field Equation of a Twisted Skyrme Strings

We construct non-linear sigma model plus Skyrme term (Skyrme model) with a twist in the gravitational field. To simplify the solution, first we examine non-linear sigma model without Skyrme term, in particular with a twist, which comprises a vortex solution with an added dependence on a twist term $mkz$, where $z$ is the vertical coordinate. We find that vortex solution for non-linear sigma model with a twist is similar with vortex solution without a twist. The work is still progress.

gr-qc↗

arXiv2017

Topological and Hopf charges of a twisted Skyrmion string

We study nonlinear sigma model, especially Skyrme model with twist (twisted Skyrmion string) where twist term $mkz$ is indicated in vortex solution. We study topological and Hopf charges of a twisted Skyrmion string. We show that the Hopf charge is exist in our twisting solutions like the twisted Skyrmion string.

math-ph↗

arXiv2016

The Gravitational Field Equations of a Twisted Skyrmion String: Numerical Solution

We study nonlinear sigma model, especially Skyrme model with twist: twisted Skyrmion string where twist term, $mkz$, is indicated in vortex solution. To add gravity, we replace $η^{μν}$ in Lagrangian system with a space-time metric tensor, $g^{μν}$, which in view of the time-independence and cylindrical symmetry of the assumed vortex solution is taken to be a function of $r$ alone. We use ode45 for numerical calculation, i.e. a tool box in Matlab to solve coupled Einstein field equations which have ordinary differential equations (ODE) form.

gr-qc↗

arXiv2015

The Gravitational Field of a Twisted Skyrmion String

In this paper we study the gravitational field of a straight string generated from a class of nonlinear sigma models, specifically the Skyrme model with a twist (the twisted Skyrmion string). The twist term, mkz, is included to stabilize the vortex solution. To model the effects of gravity, we replace the Minkowski tensor, $η^{μν}$, in the standard Skyrme Lagrangian density with a space-time metric tensor, $g^{μν}$, assumed to be static and cylindrically symmetric. The Einstein equations for the metric and field components are then derived. This work is still in progress.

gr-qc↗

arXiv2015

Mathematical modeling of the gravitational field of a twisted Skyrmion string

In this paper we study the gravitational field of a straight string generated from a class of nonlinear sigma models, specifically the Skyrme model without a twist and the Skyrme model with a twist (the twisted Skyrmion string). The twist term, $mkz$, is included to stabilize the vortex solution. To model the effects of gravity, we replace the Minkowski tensor, $η^{μν}$, in the standard Skyrme Lagrangian density with a space-time metric tensor, $g^{μν}$, assumed to be static and cylindrically symmetric. The Einstein equations for the metric and field components are then derived. This work is still in progress.

gr-qc↗

arXiv2014

Twisted Skyrmion String

We study nonlinear sigma model, especially Skyrme model without twist and Skyrme model with twist: twisted Skyrmion string. Twist term, $mkz$, is indicated in vortex solution. Necessary condition for stability of vortex solution has consequence that energy of vortex is minimum and scale-free (vortex solution is neutrally stable to changes in scale). We find numerically that the value of vortex minimum energy per unit length for twisted Skyrmion string is $20.37\times 10^{60}~\text{eV/m}$.

gr-qc↗