= Causal trapping between two spherical horizons
{title2=$\dot r\leq\frac f2\dot v-\frac{r^2|\dot\Omega|^2}{2\dot v}$}
In the regular metric $ds^2=-f\,dv^2+2\,dv\,dr+r^2d\Omega^2$, a future causal tangent has $\dot v\geq0$. For $\dot v>0$, causality gives $\dot r\leq f\dot v/2-r^2|\dot\Omega|^2/(2\dot v)$. If $f<0$ between two horizons, the areal radius must decrease. An inner event cannot reach the original exterior <future null infinity> without traversing that band in the forbidden direction.
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