Imagine a foolish astronaut who travels into a Schwarzschild black hole. It’s thought that there’s nothing special about the geometry he encounters at the Schwarzschild “radius” (OK, maybe some serious tide). But suppose he has a thermometer. What temperature does he measure?

You may assume the thermometer is either a radiometer pointed toward the black hole, or a radiometer that averages over all directions.

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    $\begingroup$ The temperature of what ? $\endgroup$ Jun 20, 2021 at 12:55
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    $\begingroup$ Is this what you want? $\endgroup$
    – J.G.
    Jun 20, 2021 at 12:59
  • $\begingroup$ @J.G. The Hawking temperature is, theoretically, what a radiometer a large distance from the black hole and at rest relative to it measures. That's not my question. $\endgroup$
    – John Doty
    Jun 20, 2021 at 13:02
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    $\begingroup$ @JohnDoty Please edit your question to say what sort of temperature you want. $\endgroup$
    – J.G.
    Jun 20, 2021 at 13:06
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    $\begingroup$ Another important thing you have to specify in this question is the frame of the astronaut. The frame where the astronaut is hovering over the black hole slightly above the Schwarzschild radius, is accelerating relative to the frame in which the astronaut plunges into the black hole along a geodesic (which is actually an inertial frame). Because of the Unruh effect, only the former astronaut would experience a thermal bath of particles. $\endgroup$
    – Andrew
    Jun 20, 2021 at 14:58