Do the energies of cosmic rays approach infinite at the event horizon of a black hole?

Question

Let's assume an observer orbits close to a black hole, he is not alone, massive cosmic rays, like electrons and protons and other kind of space dust comes from the outer space and may hit him.

Since these cosmic rays are falling down the gravitational potential well of the black hole they get accelerated and gain energy.

Does this mean an observer orbiting near a black hole will experience cosmic rays with higher energies than usual?

Since at the event horizon infinite energy would be needed to escape to a distant point, does this mean that massive cosmic rays will get accelerated to infinite energy (and tear apart everything they hit on before it could reach the singularity)?

Answer 1

I wouldn't expect the result for massive particles to be qualitatively different than the result for photons. For photons, see this question: What will the universe look like for anyone falling into a black hole? . There are red shifts at backward-looking angles, and blue shifts at forward looking angles. These shifts are finite, not infinite, even for an observer inside the horizon.

Answer 2

An orbiting observer is a bit problematic because there are no stable orbits for $r \le 3r_s$, so let's instead consider an observer hovering at some distance $r$ from the black hole. In that case as $r \rightarrow r_s$ the blue shift does indeed $\rightarrow\infty$ and the observer would indeed be roasted.

But this shouldn't be surprising. The acceleration required to hover at a distance $r$ from the black hole goes to infinity as the observer approaches the horizon, so in effect the infinite blue shift corresponds to an infinite acceleration. If you are falling freely into the black hole then the blue shift does not become infinite. In fact a freely falling observer sees the light redshifted not blueshifted.