Proton sized black hole - part 2 (or is it 3)

Hundreds of billions of years.

Good gravy, that’s one angry little black hole.

Actually, at that temperature, around 50 or 60% (depending on a point of contention about neutrino physics) of the energy would be in neutrinos, and a nonnegligible portion of the remainder will be in gravitons, neither of which would do anything to you. The bigger problem would be from the electrons and positrons. And essentially all of the photons produced, either directly or from annihilation of the positrons, would be well into the extreme gamma range, not x-ray.

I suppose I should clarify that that’s the radius, so it would be 30 billion light years across.

(Anyone wanna check my math and make sure I did that right? Dammit Jim, I’m an opera singer, not a physicist.)

And on thinking about it further, the emission in neutrinos is something of a red herring: Neutrino emission will be the major contributor to mass loss of the hole, but since the hole will last for billions of years, we don’t much care about that. Emission in the dangerous particles (photons and electrons/positrons) will be independent of the emission of neutrinos, and so the details of the neutrino physics are irrelevant to how dangerous the hole will be. By my more detailed calculations, the dangerous radiation from a 650 million-ton hole will be just about exactly 10^10 watts (9.95 GW), of which 81% will be electrons and positrons, and the remainder photons.

EDIT: Honesty compels me to admit that I fudged a bit: The figures I had lying around lumped graviton and photon emission together, so some of what I credit to photons there is actually harmless gravitons. Photons account for most of the massless particles, though.

Considering that. How close could one safely get to a 650 Million ton black hole then?