WEAK GRAVITATIONAL FIELD AROUND A GLOBAL TEXTURE

Abstract

Weak gravitational field in the asymptotic region far outside the core of a global texture is investigated without the nonlinear σ-model approximation. We solve the linearized Einstein field equations with the stress-energy tensor contributed by a spherically symmetric global texture to obtain the asymptotic form of the metric. It is shown that, even in this more general case than that of the self-similar solution in the nonlinear σ-model approximation, the metric of the spatial hyperspace in the asymptotic region is that of a flat space with a deficit solid angle whose magnitude is independent of time.