Suppose we have an event horizon H which is a light-like, closed 2-surface. Photons radiated outwards at the horizon along a light-like normal u of the horizon stay on the horizon (this is trivial b/c this statement is nothing else but the definition of the light-like 2-surface). Now suppose we disturb the horizon, e.g. via infalling matter. This will result in a "dynamical expanding horizon". By definition this horizon is a light-like 2-surface, too. Question: can one proof (or disprove) that photons trapped on the horizon will stay on the horizon even for disturbed, expanding horizons? I think this question is equivalent to the question whether "the horizon expands along the normal u". The answer is simple for Schwarzschild geometry and radially infalling shells of dust. But I don't see how to generalize this for horizons with arbitrary geometry and arbitrary perturbations.