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?

• smooth perturbations or any diffeomorphism isn't going to remove the already existing event horizon. May be you should ask whether these smooth perturbations can actually prevent the formation of trapped surfaces in the first place Commented Oct 11, 2022 at 18:49
• I guess, yes, if light could escape at some point then it would no longer be called an event horizon! Perhaps what I was imagining was some kind of pseudo event horizon which looks 99.9% like a normal event horizon except some light managed to escape. But I think such a thing does not exist.
– user84158
Commented Oct 12, 2022 at 1:54
• Unless one modified the definition to instead of light being trapped forever, it was trapped for "a very long time".
– user84158
Commented Oct 12, 2022 at 2:01
• At least, experimentally as of now no one can make a difference b/w an ideal BH and 99.99% BH, one could say wait long enough and see how it behaves. Also the area theorem ensures that the horizon can only monotonically increase under reasonable energy conditions. I feel that there could be some criterions based on known physics which can dismiss space time having ideal BH to be unphysical Commented Oct 12, 2022 at 6:11
• if it's close to but not inside the horizon, it's "possible" (i mean highly ONLY in theory) - if its inside the event horizon, no. Commented Jan 9, 2023 at 10:38

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.)