Naked singularities in dilatonic domain wall space-times

TL;DR

This work analyzes naked singularities in dilatonic domain-wall spacetimes, using a thin-wall formalism to couple a dilaton to the wall potential and exploring both exponential and self-dual dilaton couplings. It demonstrates that non-extreme and ultra-extreme walls with exponential coupling harbor naked planar singularities, while extreme walls exhibit naked or null singularities depending on the coupling parameter $\alpha$, with a special window at $\alpha=1$. The study also shows that self-dual dilaton couplings can yield singularity-free vacuum-domain-wall spacetimes, but only non-/ultra-extreme walls are dynamically stable, and extreme self-dual solutions are unstable. A cosmological correspondence maps these wall solutions to dilaton-driven FLRW cosmologies, clarifying horizons and equation-of-state behavior, and imposing significant constraints on string-inspired and supergravity theories with dilatons. Overall, the results highlight the need for nonperturbative effects to alter the spacetime structure and potentially render such theories phenomenologically viable.

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.

Figures (10)

• Figure 1: $\gamma$ versus $z$ in units of $\chi$ for extreme solutions with with $\alpha = 4$ (upper curve) and $\alpha = 6$. For $0\leq \alpha\leq 3$, the equations of state are straight lines $\gamma = 2\alpha/3$.
• Figure 2: $a$ versus $z$ in units of $\chi$ with for extreme solutions with $\alpha = 0.5$, $\alpha=1$, and $\alpha=2$, respectively. Solutions with $\alpha>1$ collapse to a naked singularity at a finite value of $z$.
• Figure 3: $a$ versus $z$ in units of $\chi$ with $\alpha = 1$ for different values of $\beta$. Starting from the left at the bottom of the figure where $a=-5$, the curves correspond to $\beta=0$, $\beta=-0.01$, $\beta=-0.1$, $\beta=0.01$, and $\beta=0.1$.
• Figure 4: $a$ versus $z$ in units of $\chi$ with $\alpha = 1/2$. The curve starting in the middle corresponds to the extreme solution. The non-extreme case with $\beta=0.01$ becomes singular shortly after $z = -4$. The third curve corresponds to the ultra-extreme case with $\beta=-0.01$. It also ends in a singularity.
• Figure 5: $\phi$ versus $z$ in units of $\chi$ with $\alpha = 1$. The straight line in the middle corresponds to the extreme solution. In the non-extreme case with $\beta=0.01$, the dilaton grows without bound shortly after $z = -2$. For $\beta=-0.01$, corresponding to the ultra-extreme case, the dilaton has a turning point and then decreases without bound as the singularity is approached.