Gramsci said:
How big must a black hole be to swallow an object of 1,5m x 3,585m x 20 cm and how far away must it be to not swallow you and everything around you?
It's for a movie a friend is doing, and I really hope that you could answer the question or otherwise give me the formula and you would make my day.
/Magnus
Assuming the smallest possible black hole is a Planck mass (about the mass of ten human ovums ..did you know at one point in your life you weighed less than a Planck mass? :O) with a radius of two Planck lengths. In other words it would initially behave like a small grain of sand and move towards the nearest massive object. In our atmosphere it would simply fall towards the centre of the Earth, gathering mass and potentially "swallowing" the whole Earth.
Hawking's theory that such a small black hole would evaporate is not proven. Hawking showed that the surface area of a black hole is proportional to its entropy. The rules of the universe are that entropy either stays the same or increases in a closed system. As a black hole increases in mass so does the surface area of its event horizon and therefore its entropy increases. The evaporation of a black hole represents a loss of entropy which is against the laws of thermodynamics.
A rough description of Hawking's radiation works like this. Virtual particles spontaneously appear in the vacuum. Normally they mutually anhilate in a very short period of time. In the strongly curved spacetime near a black hole the anti particle of a virtual pair might fall into the black hole while the normal particle escapes. The antiparticle anhilates a normal particle inside the black hole. If the virtual pair were an electron and a anti-electron (positron) then the net effect according to Hawking is that the black hole has lost the mass of one electron and an one electron escapes.
The flaw in this argument is that when a positron and an electron inside the black hole anhilate they release two high energy photons. These two photons produced in the anhilation are still inside the black hole as they can not escape. The energy of the two photons still contribute to the mass of the black hole so the black hole has not lost any mass. In fact the the black hole has gained mass while the space outside the black hole has gained an electron. Another violation of the rules of the universe (if we assume energy conservation is a rule of the universe, but admitedly that is not clear in GR)
If there is no good reason why it is the normal particle that is "repelled" by the black hole while the anti-particle is attracted to the black hole, then it is equally statistically likely that the reverse occurs. In that case the black hole gains an electron and the universe gains a positron. Note that in both cases the the black hole gains mass. If the positron that escapes in the latter case meets up with an electron that escaped in the former case, then they anhilate releasing two photons. The net effect of the former case and the latter case is that the space outside the black hole has gained two normal photons and the black hole has gained two normal photons and a normal electron from the vacuum energy. If the energy of the two escaped photons is somehow returned to the vacuum then the overall loss of energy from the vacuum is two photons worth. The space outside the black hole has gained nothing and black hole has gained an electron and two photons. So overall the vacuum has lost two photons worth of energy and the black hole has gained two photons worth of erergy and the universe as a whole has gained an electron trapped in the black hole. Hmmm.. any accountants out there want to audit that?
Until we are certain that small black holes evaporate rapidly, it would not be prudent to create black holes in colliders on Earth. :P