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Re: Formulas

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Posted by Anar on November 19, 2000 08:14:19 UTC

When a star explodes as a supernova, its remnant as I understand can be several thousand kilometers. But when it collapses to a black hole what happens? Its radius becomes smaller than the gravitational radius, or the Schwarzschild radius Rg, which is given by the formula Rg = 2GM/c^2, where c is the speed of light, M is the mass of the remnant, G is the gravit. constant. This is the formula that you wanted to know.

Let's proceed with this formula and explain why if the remnant collapses to radius smaller than Rg it becomes a black hole.

The escape velocity V(II) = root (2GM/R). If R = 2GM/c^2, then V(II) = root (2GM/(2GM/c^2)) = root (c^2) = c. Next, the moment when the remnant's radius becomes smaller than Rg the escape velocity becomes greater than c. Which means that nothing can escape the hole after crossing the event horizon - sphere of radius Rg. Certainly the radius of the black hole is MUCH smaller than the remnant's radius was.
Am I wrong in something?

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