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•• One can get an estimate for the Schwarzschild radius using the following classical argument: Consider a spherical mass of radius R and mass M. (a) Using conservation of energy, write down the classical escape speed, the minimum speed υ needed for an object to escape from the sphere’s surface to infinity. The Schwarzschild radius RS should be the value of R for which the escape speed equals the speed of light. Find an expression for RS in terms of G, M, and c. (By a happy accident, this nonrelativistic argument produces the exact relativistic answer.) (b) What is RS for a star of about 10 solar masses? (Solar mass ≈ 2 × 1030 kg.) (c) Taking RS the radius of the black hole, what would be its average density? [Note: Your answer to part (a) should suggest that one could have black holes of any mass, however small. This is correct, but it turns out that such low-mass black holes would be extremely unstable and would evaporate very quickly.]
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