Can an evaporating black hole emit protons with an energy beyond the GZK limit?

Question

There are protons reaching the earth with energies that exceed what their interaction with the cosmic microwave background should allow, the so-called GZK limit.

Could an evaporating black hole emit protons that exceed the GZK limit?

Answer 1

Could an evaporating black hole emit protons that exceed the GZK limit?

If by indicating that the BH is evaporating, you are wondering if a proton generated via Hawking radiation could,¹ at its creation, approach the GZK limit, then almost certainly the answer is no. A proton has a rest mass of about 1 GeV while the GZK limit is about 10,000,000,000 GeV, which means that the proton/antiproton would have to be moving quite fast (i.e., ultra-relativistically) in order to account for the missing energy. While my knowledge of Hawking radiation is superficial and learned a long time ago, this seems quite an unlikely scenario.

However! If the black hole has a magnetic field and a proton (generated via Hawking radiation or simply an ambient proton) follows the field, it can be accelerated to relativistic speeds. Though in order to approach the GZK limit, it has to accelerate for a long time (alternatively said, over a long distance), which means that the BH would have to be very big, which is why AGN are candidates for these GZK-limit protons.

^{1. A comment on a now-deleted answer to this question indicated that the BH would not actually emit protons (as they are not fundamental particles) but that they "...would appear as one of stable end products in decay chains. Their spectra would be far from Planckian, and the energy of the original quantum would be divided between all the particles."}