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It looks to me like the Schwarzschild metrics of a black hole (BH) yield a negative quantity for the square of light-speed for transverse waves inside the event horizon, and this says to me that they cannot propagate. Is this accepted understanding? Radially things are positive, at least.

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The whole point is that the matter field collapsed. Inside may be only radial spaghetti. It is pretty common understanding that going in to the singularity there is "spahettification", but I don't share the 'proper frame inside' picture.

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