Could we be sucked up entirely by a micro black hole?

Question

The hot question about being ripped apart in a black hole (no one can deny physics is boring!) got me thinking. If you cross the event horizon of a supermassive bkack hole, nothing noticeable will happen as the tidal force is small. Of course this will change when you fall further, this exciting feat will still happen as the rip is inevitable.

If the size of the hole gets smaller then the tidal forces around the horizon increase.

But what happens if the size gets really small? The Schwarzschild radius of the Sun is about 2.9 km. and that of the Earth is about o.88 cm. So there is enough room for me to fall through the horizon of the Sun and very little to fall through that of the Earth. The gravity of the Earth-sized hole is pretty big on a distance of, say, a few meters away, so I imagine you just get sucked up.

But now we decrease the size even further. At what point will nothing happen to me? The gravity field gets smaller and smaller but still there is an horizon, beyond which nothing returns. Will the micro hole just "take a bite of me"? Will I be sucked in entirely (which I can't imagine)?

Answer 1

If you and the black hole were the only things in the universe, then you would just be tidally shredded and then consumed extremely rapidly for a black hole of any sensible macroscopic mass. Anything bigger than about $10^{20}$ kg has a Schwarzschild radius much, much bigger than an atom, so there should be no problem in classically stuffing you into the black hole.

If you work out the tidal forces, say 1-m away from a Schwarzschild black hole, then you might be able to hold your body parts together if the black hole mass was $\sim 10^{12}$ kg or less. The accretion rate into the black hole will be approximately equal to the Bondi accretion rate which scales as the square of the black hole mass. If you do the sums then the accretion rate at $M<10^{12}$ kg is tiny/negligible (even ignoring radiation pressure, see Ding & Hao 2021, although I estimate about $<10^{-3}$ kg/s using the standard Bondi-Hoyle formula), so the black hole would exit your body and sink to the centre of the Earth, leaving you unharmed. Except such a black hole would likely be pumping out $>10^8$ W of Hawking radiation in the form of X-rays and gamma rays (e.g., see here) and thus vaporize anything that was close to it.

Thus you are going to be either shredded or vaporised. In the latter case your constituent parts at least will likely not end up in the black hole (or at least not immediately).