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Some quasars have redshifts of 4 or even greater. Redshifts can be caused by relative motions, by gravitational fields, or by the expansion of the universe. Consider the case of gravitational redshift. Using equation (9.7), compute how close to the black hole the emitting region would have to be in order to produce a redshift z = 4. Give your result in terms of the fraction of the Schwarzschild radius. Why is it unlikely that the redshifts of quasars could be explained solely by gravitational redshifts?

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