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There is few questions about particles reaching the singularity, but none of them answer my question.

Does any particle ever reach any singularity inside the black hole?

How fast does a black hole appear to decay from infalling observer's perspective?

Without the effects of SR, here on Earth, muons would decay in bigger rates (and never reach the surface) then it is observed at the surface, but as experiments show, we observe more muons reaching the surface, as a consequence of length contraction or time dilation.

From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame.

https://en.wikipedia.org/wiki/Muon

I am a little confused whether this applies in the case of a black hole, because:

  1. inside the black hole, to say the least, spatial and temporal dimensions behave oddly (some say they swap), so when the muon sees the path in front of it length contracted, then basically it is like seeing the path to tomorrow length contracted, because as often it is said, the singularity is a point in the future. So I am basically confused as to which dimension does the muon see length contracted in front of it.

What happens inside an event horizon is not that time and space swap places but rather that the labels we call Schwarzschild coordinates behave oddly inside a black hole.

Time paradox inside a black hole

  1. it is said on this site that this length contraction of the path in front of the muon leading to the singularity is really a rotation in spacetime

It hasn't really been contracted, it's just that due to the rotation in spacetime we are viewing the two ends at different times.

"Reality" of length contraction in SR

But how could we do this rotation if the dimensions behave oddly?

Just to clarify, there is very little chance that muons would enter the black hole, but for the sake of argument, lets assume that. Muons anyway are just an example, the main question is whether length contraction (caused by the relativistic speed of the particle) applies in the black hole on the path to the singularity.

Question:

  1. Do muons decay before they hit the singularity?
Árpád Szendrei
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1 Answers1

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This is too long for a comment:

I am an amateur in this field, but I think a general answer should not be possible. For a simple non rotating black hole the event horizon is the point of no return because the escape velocity from the gravitational field is larger than the speed of light. An in falling muon should decay according to the probability of decay given by its velocity and the time dilation effects. As seen in this link for atmospheric muons, one needs the specific boundary conditions, in this case the specific black hole dimensions, to see how many would survive before the singularity.

I do not think that quantizing gravity would change this .

I cannot extrapolate for charged and rotating black holes which have funny horizons.

I hope an expert replies.

anna v
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