Three Roads To Quantum Gravity

CHAPTER 7
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BLACK HOLES ARE HOT
The reason why we have been considering an accelerating
observer is that her situation is very similar to that of an
observer hovering just above the horizon of a black hole. So
the two laws we found at the end of the last chapter, Unruh's
law and Bekenstein's law, can be applied to tell us what we
see as we hover over a black hole. Applying the analogy, we
can predict that an observer outside the black hole will
see themself as embedded in a gas of hot photons. Their
temperature must be related to the acceleration the engines
need to deliver to keep the spacecraft hovering a ®xed
distance above the horizon. Furthermore, the photons that
this observer detects will be randomized because a complete
description of them will require information that is beyond
the horizon, coded in correlations between the photons she
sees and photons that remain beyond the horizon (Figure 18).
To measure this missing information she will attribute an
entropy to the black hole. And this entropy will turn out to be
proportional to the area of the horizon of the black hole.
Although the analogy is very useful, there is an important
difference between the two situations. The temperature and
entropy measured by the accelerating observer are consequences
of her motion alone. If she turns off her engines, the
photons making up her horizon will catch up with her. She
can then see into her hidden region. She no longer sees a hot
gas of photons, so she measures no temperature. There is no
missing information as she sees only empty space, which is