We propose another version of Black Hole information Paradox owing absence of Diffeomorphism symmetry for Black Hole Spacetime. The central idea is assumptions of semiclassical Gravity like locality, causality and diffeomorphism symmetry lead to another paradox. The paradox unlike many other recent versions of Information paradox is valid even at very early times. The possible suggestive way for the resolution of paradox has various approaches like validity of Black Hole Complementarity from the very begining or the principle of Holography of Information proposed by Suvrat et. al. We discuss some subtleties with these approaches in the local nature of splitting of Hilbert Space (in some pseudoprecise way) of the dual CFT. Being as conservative as we can, to avoid such subtleties (which have been addressed in the paper) we suggest that absence of Diffeomorphism symmetry for Black Hole Spacetime implies it being a smooth Finsler manifold. We will discuss what we mean by this and the implications of it. We also give a recipe for recosntructing Null Hypersurface for Black Hole Spacetime in a different way in section 3.6, 3.7 of the paper. We are also lead to notion of Finsler Geometry for Black Hole Spacetime owing to asymmetry of line element. We also find that the Null Diffeomorphism Symmetry group of 2 dimensional Minokowski spacetime admits a superspace structure. Despite analytical difficulty of solving coupled ordinary Raychaudhari differential equations and a consistency condition we verified the claim of superspace structure for Null Diffeomorphism group for Schwarschild spacetime.
| Published in | American Journal of Astronomy and Astrophysics (Volume 12, Issue 3) |
| DOI | 10.11648/j.ajaa.20251203.13 |
| Page(s) | 68-89 |
| 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. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Diffeomorphism Symmetry, Finsler Geometry, Superspace
| [1] | Lawrence Paul Horwitz, Vishnu S Namboothiri, Gautham Varma K, Asher Yahalom, Yosef Strauss, and Jacob Levitan. Raychaudhuri equation, geometrical flows and geometrical entropy. Symmetry, 13(6), 2021. |
| [2] | Sayan Kar and Soumitra Sengupta. The raychaudhuri equations: A brief review. Pramana, 69(1): 49-76, July 2007. |
APA Style
Singh, S. (2025). Absence of Diffeomorphism Symmetry for Black Hole Spacetime: A Prelude to Black Hole Spacetime Being a Smooth Finsler Manifold. American Journal of Astronomy and Astrophysics, 12(3), 68-89. https://doi.org/10.11648/j.ajaa.20251203.13
ACS Style
Singh, S. Absence of Diffeomorphism Symmetry for Black Hole Spacetime: A Prelude to Black Hole Spacetime Being a Smooth Finsler Manifold. Am. J. Astron. Astrophys. 2025, 12(3), 68-89. doi: 10.11648/j.ajaa.20251203.13
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Download@article{10.11648/j.ajaa.20251203.13,
author = {Shreyansh Singh},
title = {Absence of Diffeomorphism Symmetry for Black Hole Spacetime: A Prelude to Black Hole Spacetime Being a Smooth Finsler Manifold
},
journal = {American Journal of Astronomy and Astrophysics},
volume = {12},
number = {3},
pages = {68-89},
doi = {10.11648/j.ajaa.20251203.13},
url = {https://doi.org/10.11648/j.ajaa.20251203.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20251203.13},
abstract = {We propose another version of Black Hole information Paradox owing absence of Diffeomorphism symmetry for Black Hole Spacetime. The central idea is assumptions of semiclassical Gravity like locality, causality and diffeomorphism symmetry lead to another paradox. The paradox unlike many other recent versions of Information paradox is valid even at very early times. The possible suggestive way for the resolution of paradox has various approaches like validity of Black Hole Complementarity from the very begining or the principle of Holography of Information proposed by Suvrat et. al. We discuss some subtleties with these approaches in the local nature of splitting of Hilbert Space (in some pseudoprecise way) of the dual CFT. Being as conservative as we can, to avoid such subtleties (which have been addressed in the paper) we suggest that absence of Diffeomorphism symmetry for Black Hole Spacetime implies it being a smooth Finsler manifold. We will discuss what we mean by this and the implications of it. We also give a recipe for recosntructing Null Hypersurface for Black Hole Spacetime in a different way in section 3.6, 3.7 of the paper. We are also lead to notion of Finsler Geometry for Black Hole Spacetime owing to asymmetry of line element. We also find that the Null Diffeomorphism Symmetry group of 2 dimensional Minokowski spacetime admits a superspace structure. Despite analytical difficulty of solving coupled ordinary Raychaudhari differential equations and a consistency condition we verified the claim of superspace structure for Null Diffeomorphism group for Schwarschild spacetime.
},
year = {2025}
}
TY - JOUR T1 - Absence of Diffeomorphism Symmetry for Black Hole Spacetime: A Prelude to Black Hole Spacetime Being a Smooth Finsler Manifold AU - Shreyansh Singh Y1 - 2025/08/05 PY - 2025 N1 - https://doi.org/10.11648/j.ajaa.20251203.13 DO - 10.11648/j.ajaa.20251203.13 T2 - American Journal of Astronomy and Astrophysics JF - American Journal of Astronomy and Astrophysics JO - American Journal of Astronomy and Astrophysics SP - 68 EP - 89 PB - Science Publishing Group SN - 2376-4686 UR - https://doi.org/10.11648/j.ajaa.20251203.13 AB - We propose another version of Black Hole information Paradox owing absence of Diffeomorphism symmetry for Black Hole Spacetime. The central idea is assumptions of semiclassical Gravity like locality, causality and diffeomorphism symmetry lead to another paradox. The paradox unlike many other recent versions of Information paradox is valid even at very early times. The possible suggestive way for the resolution of paradox has various approaches like validity of Black Hole Complementarity from the very begining or the principle of Holography of Information proposed by Suvrat et. al. We discuss some subtleties with these approaches in the local nature of splitting of Hilbert Space (in some pseudoprecise way) of the dual CFT. Being as conservative as we can, to avoid such subtleties (which have been addressed in the paper) we suggest that absence of Diffeomorphism symmetry for Black Hole Spacetime implies it being a smooth Finsler manifold. We will discuss what we mean by this and the implications of it. We also give a recipe for recosntructing Null Hypersurface for Black Hole Spacetime in a different way in section 3.6, 3.7 of the paper. We are also lead to notion of Finsler Geometry for Black Hole Spacetime owing to asymmetry of line element. We also find that the Null Diffeomorphism Symmetry group of 2 dimensional Minokowski spacetime admits a superspace structure. Despite analytical difficulty of solving coupled ordinary Raychaudhari differential equations and a consistency condition we verified the claim of superspace structure for Null Diffeomorphism group for Schwarschild spacetime. VL - 12 IS - 3 ER -
Department of Physics, Harish Chandra Research Institute, Jhunsi, India
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