Cosmic strings in a generalized linear formulation of gauge field theory

TL;DR

This paper constructs and analyzes self-dual cosmic string solutions within a generalized gauge field theory framework, proving existence and asymptotic properties using advanced mathematical techniques.

Contribution

It introduces a novel generalized linear potential formulation for cosmic strings and establishes rigorous existence results for multiple string solutions.

Findings

Existence of solutions for multiple cosmic strings under certain conditions

Proven solutions for identical string centers using fixed point theorems

Derived sharp asymptotic estimates for solutions at infinity

Abstract

In this note we construct self-dual cosmic strings from a gauge field theory with a generalized linear formation of potential energy density. By integrating the Einstein equation, we obtain a nonlinear elliptic equation which is equal with the sources. We prove the existence of a solution in the broken symmetry category on the full plane and the multiple string solutions are valid under a sufficient condition imposed only on the total string number N. The technique of upper-lower solutions and the method of regularization are employed to show the existence of a solution when there are at least two distant string centers. When all the string centers are identical, fixed point theorem are used to study the properties of the nonlinear elliptic equation. Finally, We give the sharp asymptotic estimate for the solution at infinity.