Solution of Einstein’s Equations for a Closed Null String with Axial Symmetry that Is Radially Increasing Its Size

Abstract

A solution to the Einstein equations for a closed null string with axial symmetry that is radially increases its size is found. The possibility of choosing the ideal gas of null strings as a dominant source of gravity is confirmed in the study of the null string inflation mechanism in Friedmann–Robertson–Walker spaces. The absence of a limit transition between the solution that is found and the solution for a closed circular null string that is radially changing its size is shown. This indicates the stability of the configuration of a closed circular null string during its motion in an external gravitational field. It is noted that part of the characteristics of the null string gas, such as the ability to form a domain structure and existence of stable polarized states (multi-string systems), are independent of the shape of null string, but the dynamics of the test null string in a field of such multi-string system has singularities.