Schwartschild horizon for a rotating blackhole like object as a 3-D lightlike surface defining wormhole throat

The metric determinant at Schwartschild radius is non-vanishing. This does not quite conform with the interpretation as an analog of a light-like partonic 3-surface identifiable as a wormhole throat for which the determinant of the induced 4-metric vanishes and at which the signature of the induced metric changes from Minkowskian to Euclidian.

An interesting question is what happens if one makes the vacuum extremal representing imbedding of Schwartshild metric a rotating solution by a very simple replacement Φ→ Φ+nΦ, where Φ is the angle angle coordinate of homologically trivial geodesic sphere S² for the simplest vacuum extremals, and Φ the angle coordinate of M⁴ spherical coordinates. It turns out that Schwartschild horizon is transformed to a surface at which det(g₄) vanishes so that the interpretation as a wormhole throat makes sense. If one assumes that black hole horizon is analogous to a wormhole contact, only rotating black hole like structures with quantized angular momentum are possible in TGD Universe.

For details see the chapter TGD and GRT of "Classical Physics in Many-Sheeted Space-time".