22. [N, CJ Looking for Black Holes with Lasers Suppose primordial b...

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22. [N, CJ Looking for Black Holes with Lasers Suppose primordial black holes of mass ~ 1015 g were made in the early universe and are now distributed throughout space. If an observer shines a laser on a black hole some of the light is backscattered to the observer. A search for such primordial black holes could in principle be carried out by shining lasers into space and looking for the backscattered radiation. (a) Explain why some light is backscattered. From Hartle's pages 210-211: the magnitude of the total angle swept out as the light ray proceeds in from infinity and back out again so Ao = 2 (9.78) where W1 is the value of w at which the bracket vanishes. The angle AO swept out in one pass thus depends only on the ratio M/b. A plot of its behavior for large values of this ratio is shown in Figure 9.11. 2 1.5 1 it 0.5 () 0.05 0.1 0.15 0.2 M b (b) Suppose the flux of photons ((number)/m 2 s) in the laser beam is fx, the mass of the black hole is M, and it is a distance R away. Derive a formula for the number of photons per second that will be returned to a collecting area of radius d at the origin of the beam. Assume that the width of the beam is much larger than the size of the black hole. (Hint: A little numerical integration is required to get an accurate answer for this problem.) (c) Could the lasers described in Box 2.1 on p. 14 hope to detect such a black hole?

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