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My basic understanding of the Unruh effect is that an accelerating observer will experience black-body radiation proportional to the magnitude of the local acceleration, while an observer in an inertial frame will not.

If A is in an inertial frame and observes B in an accelerated frame, A must observe the effect of Unruh radiation on B?

For example B could transmit a signal at A, the increased temperature in B's reference relative to A would cause additional thermal noise in the signal. I have assumed this is true.

If A observed B falling into a gravitational well and hence being accelerated from A's perspective, would A observe the effects of Unruh radiation on B? I have assumed this to be true.

Question:

As the acceleration at the singularity of a black-hole is infinite, is it true that any path approaching it will pass through a region where the magnitude of the acceleration is high enough to cause the Unruh radiation to thermalise everything, as the temperature can get arbitrarily high? If B was falling into a black hole, would A observe this 'Unruh thermalisation'?

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Unruh/Hawking radiation only affects you if you move noninertially. Gravitational acceleration doesn't count. If you (free)fall into a black hole then you objectively aren't affected by the radiation, from anyone's perspective. If you try to avoid falling in by accelerating away then you are.

If A is in an inertial frame and observes B in an accelerated frame, [...] If A observed B falling into a gravitational well and hence being accelerated from A's perspective, [...]

A reference frame is just a coordinate system. You're in one if it covers the patch of spacetime that you're in, regardless of your state of motion. A and B will agree on whether B is accelerating (= moving noninertially = affected by the radiation) regardless of the coordinate system they pick, because that's a physical (coordinate independent) property. So this part of your assumption is false.

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  • $\begingroup$ @safesphere What happens when the hovering observer (A) decides to stop hovering and fall through the horizon? Suppose it's a Rindler horizon so there can't be a firewall. Classically, while A hovers they see B's last pre-horizon moments redshifted more and more, and when they stop hovering the redshift stops increasing and they see a smooth continuation of B's history past the horizon. If you're right, they see B burn up while hovering, and then what? $\endgroup$
    – benrg
    Aug 6, 2020 at 4:00
  • $\begingroup$ @safesphere You didn't answer my question. In whatever theory your first comment was about, is A is permanently stuck in an alternate world where B is dead, or does B come back to life somehow, and if so exactly how? Anyway, the answer is that the premise is wrong. You can analyze Unruh radiation in Minkowski or in Rindler coordinates, and you get the same result either way. You seem to think the universe forks into alternate realities depending on which coordinates you pick. No quantum gravity researcher believes that. Whatever you read that led you to believe that, you misinterpreted it. $\endgroup$
    – benrg
    Aug 6, 2020 at 17:35
  • $\begingroup$ @safesphere B sees A heat up and A doesn't see B heat up; it's objectively true that A heats up and B doesn't. The Unruh effect doesn't introduce radical subjectivity into physics. It's easy to find statements in the literature that inertial objects aren't affected, but it may be hard to find a clear statement that they're unaffected "from everyone's perspective", because that's considered obvious. You could look at Crispino et al, which derives various results in Minkowski and Rindler coordinates to show that they're consistent. $\endgroup$
    – benrg
    Aug 6, 2020 at 22:50

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