How small the earth should be for it to become a black hole

How small would the earth have to be squashed so that it would become a black hole?

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1 Answer

You can define a Schwarzschild Radius based solely on total mass, i.e. $R_s = \frac{2GM}{c^2}$. If you plug in the mass of the earth, the radius is about 9 mm --- which is how small you would have to compress it to make a black-hole.

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why is it not necessary to account for relativistic effects? – CognisMantis Jul 5 '15 at 16:24
@CognisMantis The Schwarzschild Radius is a relativistic effect. What else might one account for? – DilithiumMatrix Jul 5 '15 at 19:23
oh, sorry. I had the impression that the derivation was to have mv^2/2=GMm/r, which magically gets the right answer. Why is it not justified to use mc^2(L-1)=GMm/r, but when I do that, I get that the radius is zero. Why must we use the field equations? – CognisMantis Jul 6 '15 at 12:58