(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A sub-atomic particle is near the event horizon of a black hole. Due to the nearby gravitational field, the Ricci Curvature Tensor is changing rapidly. The particle then performs quantum tunneling.

2. Relevant equations

Which version of spacetime does the tunneling particle use? The two most obvious are following the changing curve, and following the curve fixed at its current (start of tunneling) position.

3. The attempt at a solution

This isn't a homework problem, but rather self study. I'm looking for a qualitative answer rather than an analytic one. I hope this is the right forum. If not could someone direct me?

The proper answer would of course depend on experimental measurement which, lacking a tabletop black hole, would require some subtle experimental work. I have no idea if some experiment has been done. I hope so. If not, it's an area which could yield some deep insights into how our universe works.

Some conundrums: Particles don't have fixed positions due to uncertainty. I'm weak in linear algebra (I can grind equations, but lack deep understanding). The two obvious solutions are not the only possible solutions. Further given the incompatibility of Quantum Theory and General Relativity, it is unlikely the answer will be one of those two. Finally I'm weakish in Quantum Theory and just plain weak in General Relativity.

Some further information: I was considering hyper-massive black holes. I noticed someone claimed (on wikipedia) that the radius of a black hole is linearly proportional to its mass. Thus the density goes down with the square of the mass. As the mass grows much larger the density should approach that of empty space. Also naively the surface gravity should drop as the black hole grows. But of course the actual equations are much more complex. I took this to mean the curvature got more severe near the event horizon, but that's a very shaky assumption. Still, assuming that to be the case, the curvature near the event horizon should get below the tunneling distance of sub-atomic particles (being more or less flat near the particle). At that point the black hole could speculatively no longer interact with our world except in ephemeral ways. Particles would tunnel across the event horizon (most of the time) and pop out the other side (where the black hole's density would be so low it might seem as empty space).

Before this happened though there would be a time when the black hole would eat particles randomly, passing through most, and occasionally gobbling some. This might explain quasars.

Of course this speculation is based at it's inception on many unfounded assumptions. Wikipedia must be right (it does happen sometimes). Particles must tunnel more or less according to the space time curvature of their origin (thus my question). The high curvature region must get smaller, and fast enough to get really small. The inside of a low density black hole must appear as empty space.

I'm likely wrong about most of these assumptions. But I don't know. I do want to know the answer to the original question because it is fundamental to how the universe fits together. I almost posted the rest of it in the science fiction section, but the homework faq wanted me to show my thinking.

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# A particle near an event horizon

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