Field equations and vector order parameter in brane world applications

B.E. Meierovich1

Abstract

Phase transitions with spontaneous symmetry breaking and a vector order parameter are considered in multidimensional general relativity. Field equations describing the gravitational properties of topological defects, are derived. The topological defects are classified according to the symmetry of the covariant derivative of the vector field. 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 the phase transition the solutions are found analytically. A comparison with the commonly used scalar multiplet approach demonstrates advantages of the vector order parameter.

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