Branes, moduli spaces and smooth transition from big crunch to big bang

We consider branes $N$ in a Schwarzschild-$\text{AdS}_{(n+2)}$ bulk, where the stress energy tensor is dominated by the energy density of a scalar fields map $\f:N\ra \mc S$ with potential $V$, where $\mc S$ is a semi-Riemannian moduli space. By transforming the field equation appropriately, we get an equivalent field equation that is smooth across the singularity $r=0$, and which has smooth and uniquely determined solutions which exist across the singularity in an interval $(-\e,\e)$. Restricting a solution to $(-\e,0)$ \resp $(0,\e)$, and assuming $n$ odd, we obtain branes $N$ \resp $\hat N$ which together form a smooth hypersurface. Thus a smooth transition from big crunch to big bang is possible both geometrically as well as physically.