Extensible Black Hole Embeddings for Apparently Forbidden Periodicities

TL;DR

This paper explores how extending black hole embeddings in higher dimensions can allow for forbidden periodicities, linking geometric conditions with quantum flux quantization.

Contribution

It introduces a method to achieve extendibility of black hole embeddings for certain frequencies by allowing non-trivial global embeddings in higher-dimensional spaces.

Findings

Extendibility achieved for forbidden frequencies within specific bounds.

Kruskal sheets viewed as slices in Kaluza-Klein backgrounds.

Euclidean $k$ discreteness linked to twistor flux quantization.

Abstract

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, parameterized by $k$, extendibility can be achieved for apparently forbidden frequencies $\omega_{1}(k)\le\omega (k)\le \omega_{2}(k)$. The Hawking-Gibbons limit, say $\displaystyle{\omega_{1,2}(0)= {1\over{4M}}}$ 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.