It was a interesting read JP, although some of it went far over my understanding, as relating Greens theorem to the question if information is 'stored'? Presented in the link following from the one you linked to, about black holes. Don't see how such a information would tell you if it was a apple or a orange falling in? When it comes to the question about what's inside a event horizon I don't know what to think, actually. I've also seen it defined such as everything inside a event horizon is 'the singularity', which then should makes any positional reference after passing that event horizon meaningless, applying the shell theorem. To me it makes sense to consider the inside of a event horizon as having a spatial existence, with a center, as defined from a 'inside'? This assumes that infalling matter do pass a event horizon though. If it doesn't?

But the Green theorem applied as a proof for information being stored is what really confuses me.

"There is a final alternative, however. It is possible that the fluctuations of the event horizon itself would store the impressions of the incoming (or outgoing) particles. Note that this requires the projection of the information in a four-dimensional space (three spatial dimensions plus time) onto a three-dimensional space (the surface of the event horizon is a two-dimensional surface, which again changes over time), but this poses no problem, and has sound mathematical justification; for a sufficiently "well-behaved function" on a space, the behavior of the function within a region is completely determined by the values of the function on its boundary. This result is known as Green's theorem"

The Green of Green Functions.