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 C0 structure, and the assumption of smoothness as a C∞ 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.
| Published in | American Journal of Astronomy and Astrophysics (Volume 13, Issue 1) |
| DOI | 10.11648/j.ajaa.20261301.14 |
| Page(s) | 45-58 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Black Holes, Stratified Geometry, Fiber Bundles, Null Hypersurfaces, Horizon Smoothness, Causal Structure
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APA Style
Singh, S. (2026). Stratification and Related Ideas for Understanding the Smoothness of Black Hole Horizons. American Journal of Astronomy and Astrophysics, 13(1), 45-58. https://doi.org/10.11648/j.ajaa.20261301.14
ACS Style
Singh, S. Stratification and Related Ideas for Understanding the Smoothness of Black Hole Horizons. Am. J. Astron. Astrophys. 2026, 13(1), 45-58. doi: 10.11648/j.ajaa.20261301.14
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Download@article{10.11648/j.ajaa.20261301.14,
author = {Shreyansh Singh},
title = {Stratification and Related Ideas for Understanding the Smoothness of Black Hole Horizons
},
journal = {American Journal of Astronomy and Astrophysics},
volume = {13},
number = {1},
pages = {45-58},
doi = {10.11648/j.ajaa.20261301.14},
url = {https://doi.org/10.11648/j.ajaa.20261301.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20261301.14},
abstract = {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 C0 structure, and the assumption of smoothness as a C∞ 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.},
year = {2026}
}
TY - JOUR T1 - Stratification and Related Ideas for Understanding the Smoothness of Black Hole Horizons AU - Shreyansh Singh Y1 - 2026/03/18 PY - 2026 N1 - https://doi.org/10.11648/j.ajaa.20261301.14 DO - 10.11648/j.ajaa.20261301.14 T2 - American Journal of Astronomy and Astrophysics JF - American Journal of Astronomy and Astrophysics JO - American Journal of Astronomy and Astrophysics SP - 45 EP - 58 PB - Science Publishing Group SN - 2376-4686 UR - https://doi.org/10.11648/j.ajaa.20261301.14 AB - 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 C0 structure, and the assumption of smoothness as a C∞ 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. VL - 13 IS - 1 ER -
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