In classical general relativity, one can think of an event horizon a tube of light cones in (3+1)D Minkowski space-time, in which the future-cone of each lightcone is inside the 4D region and the past-cone of each lightcone is outside the 4D region. Thus creating a one-way surface that light can enter but can't escape.
But we know that on very small scales, the light-cones are unlikely to line up quite so neatly.
Is it possible to prove that no smooth perturbation of Schwarzschild event horizon will ever create an escape route for light to escape? (One could imagine jiggling the light cones near the event horizon such that they look fairly chaotic). But in a smooth manner so neighbouring light-cones line up. i.e. the metric still has to be differentiable.
On the other hand, is it possible to prove that a discrete jump in the direction of two light-cones at neighbouring points in space near the horizon, i.e. the metric is not a continuous function at some point, would provide a place on the event horizon where light could escape?
In other words is it possible to prove that event horizons require smoothly differentiable metrics?