Could light escape a chaotic event horizon? 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?
 A: By definition, no.  An event horizon is defined to be the boundary of a region of spacetime from which light cannot escape to infinity.  This means that if a photon gets to infinity from a particular spacetime event, that spacetime event was not inside the event horizon.
A counterintuitive property of this definition, by the way, is that it's non-local.  The definition of where an event horizon is depends on the entire future of the spacetime;  if something happens "in the future" that allows light to escape to infinity from an event $A$, then that event is "retroactively" defined to not be in the event horizon.  (The quotes are because the whole notion of "past" and "future" are a bit hand-wavy here.)
An extreme example of this is Oppenheimer-Snyder collapse, a toy model in which a thin shell of dust collapses into a black hole.  It is possible to show that the spacetime inside the shell is completely flat (as we might expect from the Newtonian analogue.)  But there are regions of spacetime inside the collapsing shell, at times well before the shell collapses to a point, which are inside the event horizon — because in the future, the dust shell is going to fall past these points and pull any light rays back in to the central singularity that will eventually form.
