> The concern for the first jumper is ... whether it can be thrown hard enough and accurately enough for the second to ever reach it. The concern for the second is whether the first can catch his ball without exploding like a paper sack full of wet spaghetti.
This is just a practical difficulty. There might actually be stronger constraints in play -- the two jumpers might be causally disconnected from one another entirely (that is, their forward light cones might intersect only at the singularity.) I have no idea whether that's possible, though.
> If you aimed correctly, you could send messages to your older self, but I'm not entirely certain if your older self could reply.
Any message has to be received "lower" than where it was sent, so all messages go from younger selves to older selves.
Which would also imply that you cannot communicate with a person who jumped in right after you did. I think your model does not account for the jumper having mass and his communication photons being massless.
The reason the photons cannot escape is not because they are affected by the gravity, but because the space they must traverse is stretched and twisted to such an extent that to an observer inside the event horizon, the entire outside universe presents an infinitesimally small target that is receding rapidly. Anything you might manage to shoot out would be indistinguishable from the Hawking radiation coming from the event horizon.
On a closer scale, you could probably communicate uphill, but the conversation would be like an ent talking to a chipmunk. At some point, you simply can't target your uphill counterparty accurately enough, or with enough bandwidth to hold their interest.
> Which would also imply that you cannot communicate with a person who jumped in right after you did
That doesn't follow at all. It's conceivable we could drop three things into a black hole one after another, and at some point the first two could send a message to each other, and so could the last two, but the first and last could not (in a situation similar to the cosmological horizon.)
> the entire outside universe presents an infinitesimally small target
No. There is literally no direction you could fire a photon that could take it out of the black hole. You can talk to someone falling behind you only because they can "fall onto" your transmissions. Light cannot go uphill at all.
If you can communicate with someone who jumped in one second after you, you could communicate with your younger self via a gravity-warped path that has the same distance as the direct distance between you and the second jumper.
There are no one-way trapdoors with massless particles. If a photon can get in, an anti-photon (aka a photon) following the reverse trajectory (including moving backward through time) can get out. It seems almost tautological, but the photon doesn't really care which way the time arrow points, and can't tell whether it is coming or going.
The warping of spacetime is such that no photon crossing the event horizon from the outside can return to the outside. All straight light paths between any arbitrary point on the event horizon and any arbitrary point inside it do not intersect any other point on the event horizon. If your point of origin is inside the event horizon, you can fire a photon out of it. But you literally need a perfectly accurate and perfectly predictive model of all mass in and around the black hole to make the shot. A single neutron unaccounted for could bend the spacetime that the photon traverses in such a way that it misses the event horizon. So for all practical purposes, you cannot ever be certain if your photon made it out or not, especially after your first second beyond the event horizon.
There's also the little matter that your photon, if it does make it out, may have done so billions of years later, and possibly with a wavelength longer than the diameter of the event horizon, which might make it appear as though it were radiating from the event horizon itself, rather than somewhere inside. It would convey no information across. It would probably look exactly like the Hawking radiation.
> But you literally need a perfectly accurate and perfectly predictive model of all mass in and around the black hole to make the shot
I think where you're going wrong is assuming that gravity acts by "distorting angles". Like, near a massive object, maybe more than 180 degrees point downwards, and less than 180 point upwards. In a black hole, then, maybe 360 degrees (minus epsilon) point downwards, and there's a peephole pointing back up. You might litter breadcumbs along that trail, or unspool some twine to find your way back.
Alas, that's not the picture we have. It's closer to the truth to say that gravity gives space a "base velocity" (downwards) equal to the escape velocity at that point. Inside the Schwartzchild radius that velocity is higher than the speed of light, and because you can't go faster than light you can't get out.
This is just a practical difficulty. There might actually be stronger constraints in play -- the two jumpers might be causally disconnected from one another entirely (that is, their forward light cones might intersect only at the singularity.) I have no idea whether that's possible, though.
> If you aimed correctly, you could send messages to your older self, but I'm not entirely certain if your older self could reply.
Any message has to be received "lower" than where it was sent, so all messages go from younger selves to older selves.