Asymptotic stability in geometric sigma-models

Abstract

Geometric sigma-models have been defined as purely geometric theories of scalar fields in interaction with gravity. By construction, these theories possess soliton solutions with topologically nontrivial scalar sectors. We perform a detailed analysis of the stability of the effective scalar field theory far from the soliton core. It is shown that the requirement for the asymptotic stability is consistent with the existence of massive, static, spherically symmetric soliton solutions.