1/2 kilogram black hole: thought experiment

[Thetes]

Greetings! Would this be a fair estimate to the radius of a black hole?

Assumptions: The equation for escape velocity is adequate for calculation of black hole radius.
\upsilon = \sqrt{\frac{2M}{r}}
Working from there, setting the desired velocity faster than light would mean nothing could get out. So, let \upsilon = 3*10^{8} and M = \frac{1}{2}
then 3*10^{8} = \sqrt{\frac{1}{r}}
so r = 9*10^{-16}

Could we then say anytime 1/2 kilograms are within a neighborhood of 9*10^{-16} meters there is a black hole?

 

[Curl]

I don't think a 1/2 kg black hole can exist.

 

[phinds]

I don't think a 1/2 kg black hole can exist.

My understanding is that black holes smaller than that can exist, although though apparently they evaporate very quickly.

 

[Ryan_m_b]

I'm pretty sure that black holes can exist at any mass but they evaporate almost instantly. Using this nifty black hole calculator we see that a black hole of 500 grams would have a radius of just 1,832,716 plank units (7.424258e-28 metres) and would exist for just 1.050898e-17 seconds.

 

[That one guy]

This might help.

http://www.physorg.com/news/2011-05-mini-black-holes-atoms-earth.html

 

[jnorman]

ryan - if you are assuming the small BH exists in its own universe by itself, it may evaporate due to hawking radiation. however, in a universe filled with trillions of stars, cosmic dust, etc, any BH will be constantly bombarded with radiation, which adds energy/mass, as well as absorption of dust etc, which also adds energy/mass, which will greatly overcome any mass lost to hawking radiation. it will not evaprorate - it will only continue to grow.

 

[Ryan_m_b]

ryan - if you are assuming the small BH exists in its own universe by itself, it may evaporate due to hawking radiation. however, in a universe filled with trillions of stars, cosmic dust, etc, any BH will be constantly bombarded with radiation, which adds energy/mass, as well as absorption of dust etc, which also adds energy/mass, which will greatly overcome any mass lost to hawking radiation. it will not evaprorate - it will only continue to grow.

Well that depends on what media it is in doesn't it? For example if I create a hypothetical 1 gram black hole in an insanely powerful particle accelerator then it would evaporate in just 8.407183e-26 seconds, long before it passed through the accelerator's vacuum and hit the wall, even at traveling at near light speed.

Even floating in space it would be hard pressed to find anything, IIRC the density of interstellar space is somewhere near two hydrogen atoms per cubic metre.

 

[Thetes]

Thanks for the references, and sorry I left out a term (G) in the original equation as well.

\upsilon = \sqrt{\frac{2M}{r}}
/QUOTE]
should have been \upsilon = \sqrt{\frac{2GM}{r}}
Then letting \upsilon = c (rather than the earlier rounding) gives a much lower result mentioned by Ryan_m_b.

Thanks for the help clearing it up! It's amazing that Newton's formula would predict such a situation.