Extensible embeddings of black-hole geometries

Removing a black hole conic singularity by means of Kruskal representation is equivalent to imposing extensibility on the Kasner-Fronsdal local isometric embedding of the corresponding black hole geometry, Allowing for globally non-trivial embeddings, living in Kaluza-Klein-like M₅ × S₁ (rather than in standard Minkowski M₆) and parametrized by some wave number k, extensibility can be achieved for apparently "forbidden" frequencies ω in the range ω₁(k) ≤ ω ≤ ω₂(k). As k → 0, ω_{1, 2}(0) → ω_H (e.g., ω_H = 1/4M in the Schwarzschild case) that the Hawking-Gibbons limit is fully recovered. The various Kruskal sheets are then viewed as slices of the Kaluza-Klein background. Euclidean k discreteness, dictated by imaginary time periodicity, is correlated with flux quantization of the underlying embedding guage field.