I forgot about this thread - apologies.
alexchamp29 said:
But I know this is very wrong lol. Again my knowledge of physics and math is very limited. I was just curious about this scenario.
I think your analysis isn't correct even in Newtonian physics. You seem to be imagining an orbiting particle intersecting a radially infalling object. But the energy in that case isn't completely available for a merger, because the particles don't stop (at least, not in the frame you are working in), so a lot of the energy is carried away as kinetic energy.
A better scenario would be two particles moving in circular orbits in opposite directions. Then if they are identical and collide then they stop and all of the energy is available for the merger. The answer is that this is trivially possible - the closer one gets to an "orbital radius" of ##3GM/c^2##, where ##M## is the mass of the hole, the closer the kinetic energies of the particles get to infinity. So there must exist a circular orbit where two counter-orbiting particles would have enough energy to fuse.
However, that leads to the question of exactly where these particles got their energy from. They're just spinning round in circular orbits, and then they collide. Why are they in those orbits?
Perhaps a better question is, what happens if we drop two particles from infinity in orbits that graze that ##3GM/c^2## radius, and collide there? If so, I think the energy available (from the loss of gravitational potential) is ##2\sqrt{3}mc^2## (
edit: ##2(\sqrt 3-1)mc^2## actually - see post #14), where ##m## is the mass of one particle. If that's enough for fusion, you'll get fusion.