Extensible Black Hole Embeddings for Apparently Forbidden Periodicities

Imposing extendibility on Kasner-Fronsdal black hole local isometric embedding is equivalent to removing conic singularities in Kruskal representation. Allowing for globally non-trivial (living in $M_{5}\times S_{1}$)embeddings,parameterizedby$k$, extendibility can be achieved for apparently forbidden frequencies ${\omega }_1(k)\le \omega (k)\le {\omega }_2(k)$. The Hawking-Gibbons limit, say ${\displaystyle {\omega }_{1,2}(0)=\frac{1}{4M}}$ for Schwarzschild geometry, is respected. The corresponding Kruskal sheets are viewed as slices in some Kaluza-Klein background. Euclidean $k$ discreteness, dictated by imaginary time periodicity, is correlated with twistor flux quantization.