Stratification and Related Ideas for Understanding the Smoothness of Black Hole Horizons

In recent work by the author it was found that there is an absence of diffeomorphism symmetry for black hole horizons constrained by the causal structure of spacetime. This absence puts stringent constraints on the black hole spacetime manifold, topology, and smoothness. In particular, it suggests that such manifolds may have only continuity of data but no differentiability. In mathematics, this is described as a spacetime manifold with a Csup0/sup structure, and the assumption of smoothness as a Csup∞/sup structure might not hold. Previously, we supposed that the spacetime manifold may have a Finsler structure and might not be a homogeneous manifold, thus requiring new insights to study black hole spacetime. Investigating the spacetime manifold picture, we presume a mathematical concept called stratification of spacetime with smooth gluing of manifold data as an essential criterion for understanding the topology of black hole spacetime. In basic terms, stratification is a way of gluing spacetime into a collection of disjoint regions called strata such that the strata themselves are smooth, but the whole manifold may or may not have a differentiable structure. The topology of the spacetime manifold then depends on the criteria used for the process called stratification of spacetime. We investigate these and relatable ideas further in this paper. For smooth readability, we have referenced relevant literature grouped by topics or subtopics throughout the text.