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
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.
(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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