Today I have had something of an epiphany; I have been trying to prove that the central singularity of current black hole theory is false. I now realise that this ambition is futile. If you start off with the basic assumption that you can sail through the event horizon in free fall, according to the equivalence principle, then the centre is inevitably the final destination unless new physics intervenes. If there is an error in this thinking, it has to be the assumption that the equivalence principle applies, and not in the conclusion that follows.

There are two alternatives to this:  

  1. the equivalence principle does not apply when there is a change of state
  2. time stands still at the event horizon

Take these in turn: we do not apply the equivalence principle when a falling workman hits the ground as there is a change of state. We can argue against this by saying that in this case, the ground imposes fresh (em) forces and this is what breaks the equivalence principle. In the case of a black hole, the only forces involved are gravitational.

In the second case, time stands still in Schwarzschild coordinates. In trying to argue that this must be true in all coordinate systems, I am guilty of applying the rules of general relativity to a point at infinity and this is not a part of the set of real numbers and so is excluded from consideration. They then try to argue that the infinity in Schwarzschild coordinates is not physical and so can be safely ignored.

Once again the arguments are circular and thus self-fulfilling. 

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