We solved Problem 12.16 incorrectly: we used the formula for the second cosmic velocity for light, which was derived from non-relativistic expressions for kinetic and potential energies. Try to derive a formula for the radius of a “black hole” from relativistic considerations. 12.16. If the mass of a star is more than three times the mass of the Sun, then as it cools, it can shrink so much that it cannot radiate—neither a particle of matter nor light can escape from its gravitational field. Estimate the radius of such an object (“black hole”).

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