Naked singularities in dilatonic domain wall space-times.

Abstract

We investigate gravitational effects of extreme, non-extreme and ultra- extreme domain walls in the presence of a dilaton field. The dilaton is a scalar field without self-interaction that couples to the matter po- tential that is responsible for the formation of the wall. Motivated by superstring and supergravity theories, we consider both an exponential dilaton coupling (parametrized with the coupling constant alpha and the case where the coupling is self-dual, i.e. it has an extremum for a fi- nite value of the dilaton. For an exponential dilaton coupling, extreme walls (which are static planar configurations with surface energy density sigma_ext saturating the corresponding Bogomol'nyi bound) have a naked (planar) singularity outside the wall for alpha>1, while for alpha smaller or equal to 1 the singularity is null. On the other hand, non-extreme walls (bubbles with two insides and sigma_non > sigma_ext and ultra-extreme walls bubbles of false vacuum decay with sigma_ultra < sigma_ext always have naked singularities. There are solutions with self-dual couplings, which reduce to singularity-free vacuum domain wall space--times. However, only non- and ultra-extreme walls of such a type are dynamically stable.