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For the sake of this question we are inside the EH and a sound wave enters from our perspective as the sound moves closer to us at the EH would it speed up.

Specifically how would the extreme expansion of physical space lower the frequency of an incomming sound wave?

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This type of question is not constructive--- you need to understand the qualitative features solutions of General Relativity that predict black holes--- the Schwartzschild and Reissner Nordstrom solutions at the very least, to make a good question about it. This question misunderstands the nature of the singularity, imagining it as a point of infinite density at the center. This is not a good picture--- it's a surface of final time at the center of the Schwartzschild solution, and what happens there is only resolved in string theory. – Ron Maimon May 8 '12 at 5:43
@RonMaimon: There seems to be a correlation of the propagation of sound and the density of the material. Would we need to adjust the frequency of the sound wave? – Argus Jul 23 '12 at 4:27

You can't be inside the singularity, the singularity in the standard neutral non-rotating black hole is spacelike, meaning, generally speaking, that it is not a place but a time (the position and time reverse character inside the horizon). The sound waves move sideways relative to the singularity, and don't get closer or further, just sideways, and hit the singularity at the same time. The answer is just no.

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Of course all this is relative an outside observer can never view an object cross the horizon but if I was falling in I would not stop of course I could not tell you I was still falling. – Argus May 8 '12 at 5:53
@Argus: This is all interior picture, not an outside picture. The singularity is inside the horizon. – Ron Maimon May 8 '12 at 6:00
this makes me think the event horizon is the singularity or a shell were inside time progress based on how the black hole is moveing through space? – Argus May 10 '12 at 4:24
Argus: Sort of--- the horizon can be a singularity in exterior coordinates, and the interior is reconstructed from the exterior in all cases. But the time progression on the inside is not dependent on the motion of the black hole, just on what fell in, on how big it is. This is best clarified by working out the properties of the Schwarzschild solution presented in all GR books. – Ron Maimon May 10 '12 at 5:37

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