> That means the gamma factor is now (to a very good approximation) 500 (rest mass 2M times gamma of 500 times v approximately 1 gives momentum 1000M), which still corresponds to an ultrarelativistic velocity.
OK, I see your point. At those speeds a tremendous reduction in speed-energy (AKA relativistic mass) is only a small reduction in speed.
> the faster the hole is traveling, the lower the cross section will be.
At these masses gravitational attraction (that could pull in matter if given some time) is basically nil. I am assuming direct front-end collisions between the black hole and matter, so the speed doesn't make much difference.
Although thinking about it, I suspect the cross section (event horizon radius) of a proton massed black hole would be smaller than a neutrino.
> I am assuming direct front-end collisions between the black hole and matter, so the speed doesn't make much difference.
Ah, ok; yes, in this approximation (which I agree is a pretty good one--there is another subthread on this that I've been posting in), the number of particles eaten is basically the number of atoms that can be lined up end to end across the diameter of the Earth (in the worst case scenario where the hole flies straight down through the Earth). That number is about 10^17, which is many, many orders of magnitude less than the number of atoms in Mount Everest (the very rough back-of-the envelope number I come up with for that is 10^40).
> I suspect the cross section (event horizon radius) of a proton massed black hole would be smaller than a neutrino.
I thought the hole's mass was assumed to be about that of Mount Everest, at least for this discussion. The horizon radius of such a hole would be about 1.5 x 10^-14 meters, or about the size of a large atomic nucleus. I'm not sure we have a good number for the "size" of a neutrino.
Ah, ok. A black hole with the mass of a proton would have a horizon radius of about 10^-54 meters, i.e., about 19 orders of magnitude smaller than the Planck length. Of course, that is a classical calculation; when quantum gravity effects are taken into account, it's quite possible that a black hole with a horizon radius of less than one Planck length could not exist.
OK, I see your point. At those speeds a tremendous reduction in speed-energy (AKA relativistic mass) is only a small reduction in speed.
> the faster the hole is traveling, the lower the cross section will be.
At these masses gravitational attraction (that could pull in matter if given some time) is basically nil. I am assuming direct front-end collisions between the black hole and matter, so the speed doesn't make much difference.
Although thinking about it, I suspect the cross section (event horizon radius) of a proton massed black hole would be smaller than a neutrino.