Suppose a black hole size of a proton appeared.Would it take it a lot of time to suck up a pen and eventually earth? What formulae should i use to calculate that?
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$\begingroup$ I'm no expert, but I think a black hole that size would evaporate before it could suck up anything. $\endgroup$– Benjamin Rogers-NewsomeCommented Jan 26, 2018 at 18:13
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$\begingroup$ @BenjaminRogers-Newsome why so? $\endgroup$– MuradCommented Jan 26, 2018 at 18:15
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$\begingroup$ see en.wikipedia.org/wiki/… $\endgroup$– anna vCommented Jan 26, 2018 at 18:15
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$\begingroup$ It is to do with the ideas of black hole thermodynamics in that a small black hole will have a very high hawking radiation temperature, and so will radiate heat away very quickly and as a result, will evaporate in a small amount of time. $\endgroup$– Benjamin Rogers-NewsomeCommented Jan 26, 2018 at 18:17
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$\begingroup$ @BenjaminRogers-Newsome thanks for the explanation $\endgroup$– MuradCommented Jan 26, 2018 at 18:40
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1 Answer
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As comments have already mentioned, black holes that small are not thought possible. We do not have a complete theory of quantum gravity and we'd need that to make more definitive statements, but there are no reasons to think such extremely small black holes can exist.
Black Holes Don't Suck.
Black holes are just massive objects which have gravitational fields just like any other massive object. The only exceptional thing about them is that, as the mass is concentrated into such a dense region, they form an event horizon and this means they have rather extreme gravitational effects near the horizon that "everyday" objects like planets and stars do not normally show.
You can happily orbit a black hole. You can pass it by very closely and in principle get away again if you're traveling fast enough.
Which means we don't have handy equations telling us how fast black holes suck matter in.
How fast an object would approach a black hole's event horizon is going to depend on where you look from (relativity) and the distances and mass of the object involved (just like normal falling in a gravitational field).
The potential energy between say an electron and a proton is dominated by the electromagnetic force between them (the gravitational potential is much, much smaller at all ranges).
As we know that what is most likely to happen when an electron approaches a proton is that they either whizz by each other (scatter) or they form a Hydrogen atom, which is stable, not a black hole and not likely to ever become one, the electron is unlikely in the extreme to merge with the mythical proton black hole.
And the protons in any material are repelled by the positive charge of the proton black hole. That repulsion is, again, far greater than the gravitational force between proton and proton so a proton, except under extreme conditions, won't merge with the proton black hole either.
As we don't have a definitive theory involving gravity at the quantum level we can't be absolutely certain what will happen, but experiments don't show any evidence of black holes forming in e.g. LHC collider experiments.
You'll be happy to know that the mad lunatics at CERN (and they say you have to a little mad to work there :-) ) are apparently not quite mad enough to create mini black holes. They have a document explaining this. One presumes that anyone at CERN making a mini black hole will get a very nasty letter from HR. :-)
answered Jan 26, 2018 at 18:58