[deleted]
Hi Peter,
I left this for Alan on this blog site on Mar. 7, 2011 @ 14:58 GMT:
Hi Alan,
We may be thinking along parallel lines.
If a Black Hole is static (I'm not sure that it can really exist, but consider the question), then quantum gravity may build a spacetime lattice similar to a Carbon-60 buckyball/ soccer ball/ truncated icosahedron just outside of and surrounding the singularity. This symmetry could potentially be stable against the crushing gravitational (near?) singularity.
If we have a rotating Black Hole, then torsion from the spinning Black Hole may cause a pair of nested Buckyballs to morph into their homotopic cousin, a lattice-like torus. This lattice-like torus has some similarities with your Mobius figure.
I was worried about how discrete toroidal lattices could transition into continuously differentiable spacetime, but it may be as simple as Philip Gibbs "qubits of strings" idea. Basically, the lattice point is the end of a string (and the strings expand within the Black Hole as Sreenath's logarithmic spirals), and a large number of lattice points and strings exist (10^41 or more) such that spacetime seemingly blends into a continuum.
Perhaps we are all thinking along parallel lines? I had some other comments that tied into Alan's Archimede's Screw idea as well.
Have Fun!
Dr. Cosmic Ray