Vector order parameter in general relativity. Covariant equations

TL;DR

This paper derives covariant equations for vector order parameters in general relativity, classifies topological defects, and presents new solutions relevant to brane world models, including analytical solutions near phase transitions.

Contribution

It introduces covariant equations for vector order parameters, classifies topological defects, and provides new Einstein solutions with a transverse vector order parameter.

Findings

Derived covariant equations for topological defects.

Classified defects based on symmetry of the covariant derivative.

Presented new Einstein solutions with a transverse vector order parameter.

Abstract

Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are derived. The topological defects are classified in accordance with the symmetry of the covariant derivative of the vector order parameter. The abilities of the derived equations are demonstrated in application to the brane world concept. New solutions of the Einstein equations with a transverse vector order parameter are presented. In the vicinity of phase transition the solutions are found analytically.