2023/09/11 by Lei Cao, Cao, Lei, Shouxin Chen +1
Physics and Astronomy · Mathematics · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2309.05348
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.