[plfbenya] Falling into a black hole at very high speed

Start with an object at rest a good distance away from a black hole.  Allow the black hole's gravity to pull the object into the black hole.  How fast is the object traveling just before it falls in, just before it crosses the event horizon?

Qualitative answer: It is traveling just slightly less than the speed of light.  We can derive this answer by imagining running the experiment in reverse.  Start slightly outside of the event horizon.  From here, how fast do you need to launch the object upwards so that it barely makes it to that original starting point a good distance away (then starts falling downward again)?  The escape velocity at the event horizon is the speed of light, so the answer will be just slightly less.  (Why is this reasoning valid?  I'm not willing to trust that things true in Newtonian mechanics are true near black holes.  For example, general relativity does not obey conservation of energy.)

Quantitatively, what is the escape velocity as a function of distance above the event horizon?  It might be tricky even to express the answer, because speed is distance/time, and distances and time are warped near a black hole.

(How fast is a dropped-in object traveling just after it crosses the event horizon?  Is it traveling slightly faster than the speed of light?)

A black hole therefore provides an easy way to accelerate things to very close to the speed of light.  Particle physicists like accelerating things to very close to the speed of light.  Instead of dropping things straight in, consider an accretion disk.  Just outside the event horizon, are very high energy particle collisions occurring?  How high energy?  At what collision rate?  Is the collision energy much higher than that achievable by terrestrial particle accelerators?  Are the energies Grand Unified Theory scale?  Theory Of Everything scale?

Hopefully we aren't defeated by matter in an accretion disk all tending to orbit going the same direction, so collisions aren't head on.  We do know that collisions with energy high enough to produce X-rays are occurring.  Does the fact that rotating black holes have ergospheres affect the energy of collisions?  (When we observe radiation from a black hole accretion disc, how much of it is coming from within the ergosphere?)

Artificially constructing a GUT- or TOE-scale particle accelerator seems mind-bogglingly difficult; we probably won't have the technology to do so for a long while.  Sending a probe out to observe a black hole seems much easier.  We will have to wait a while (the nearest currently known black hole, HR 6819, is 1100 light years away) (update: the system is more likely a spectroscopic binary of two stars, no black hole), but it could still be faster than developing the technology to build huge particle accelerators.   (Even more optimistically, all we might need is a sufficiently powerful telescope, but that won't be able to observe particles which decay quickly, so we won't consider this any further.)

Is it better to use a large black hole or a small one for these kinds of observations?  Do we want a black hole without much of an existing accretion disk so that we can actively drop stuff in in a controlled fashion?  What kind of sensors are required?  We will probably need to separate out the particle collisions we care about from those we don't, same as with a man-made particle accelerator.  How does the strong gravitational redshift near the event horizon affect observations?

If super exotic TOE-energy particles are being produced just outside the event horizon, how do they affect things in that area?  What might they be doing quantumly to the structure of spacetime?  The region just above the event horizon might be geometrically quite complicated.  This is superficially similar to fuzzballs, but our complexity arises only when there is an accretion disk.

Could exotic particle physics occurring just outside an event horizon produce ultra high energy cosmic rays?  This could explain how they can violate the GZK limit: they only needed to travel from a "nearby" black hole.

The Theory Of Everything is of course the Holy Grail of physics.  After that, the universe is solved.  It's fascinating to believe that the Ultimate Answer to Life, the Universe, and Everything is gettable without too much difficulty, requiring mostly only patience.  The universe in fact directly gives us the answer, naturally constructing black holes with accretion disks for us to go observe.  Many black holes are giant beacons, the brightest lights in the universe, seemingly calling attention to themselves, making it impossible for us not to notice them, beckoning us to consider visiting them to observe them and learn the final secret of the universe.

(The Star Trek novel The Entropy Effect begins with observations of a black hole that mysteriously seem to indicate that something has gone very wrong with the entire universe -- the heat death of the universe will occur within a century.  (The novel's black hole was a naked singularity, having no event horizon.)  It is not unrealistic that observations of a black hole (even a normal one clothed in an event horizon) could yield profound insights about the entire universe.)