Naked singularities in dilatonic domain wall space-times.

We investigate gravitational effects of extreme, nonextreme, and ultraextreme domain walls in the presence of a dilaton field \ensuremath{\varphi}. The dilaton is a scalar field without self-interaction that couples to the matter potential 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 \ensuremath{\alpha}) and the case where the coupling is self-dual; i.e., it has an extremum for a finite value of \ensuremath{\varphi}. For an exponential dilaton coupling (${\mathit{e}}^{2\mathrm{\ensuremath{\surd}}\mathrm{\ensuremath{\alpha}}}$ \ensuremath{\varphi}), extreme walls (which are static planar configurations with a surface energy density ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ext}}$ saturating the corresponding Bogomol'nyi bound) have a naked (planar) singularity outside the wall for \ensuremath{\alpha}g1, while for \ensuremath{\alpha}\ensuremath{\le}1 the singularity is null. On the other hand, nonextreme walls (bubbles with two insides and ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{non}}$g${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ext}}$) and ultraextreme walls (bubbles of false vacuum decay with ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ultra}}$${\mathrm{\ensuremath{\sigma}}}_{\mathrm{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 ultraextreme walls of such a type are dynamically stable.