Consistent Regularization of Signature-Changing BTZ Black Holes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912790710583296 |
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| author | Milani, Farzad |
| author_facet | Milani, Farzad |
| contents | Spacetime singularities represent a fundamental challenge in gravitational physics. We present a mathematically consistent framework for signature-changing black holes based on the $(2+1)$-dimensional BTZ metric, where the signature transitions from Lorentzian $(-,+,+)$ to Euclidean $(+,+,+)$ at the horizon. We identify and rectify a critical inconsistency in previous regularization schemes concerning second-order distributional terms $\varepsilon''(r)$, introducing a \emph{modified Hadamard regularization} that respects distribution theory. This produces a vacuum solution free of surface layers and impulsive gravitational waves. Geodesic analysis reveals that radially infalling observers require infinite proper time to reach the horizon, effectively preventing access to the would-be singularity while maintaining finite curvature invariants throughout the spacetime. We further establish the physical robustness of the geometry by demonstrating linear stability against gravitational perturbations, showing that quantum scalar field propagation remains unitary and well-defined across the signature change, and reinterpreting the $r=0$ region as a topological boundary rather than a curvature singularity. Our work establishes atemporality via signature change as a mathematically rigorous mechanism for \emph{singularity avoidance} in black hole spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Consistent Regularization of Signature-Changing BTZ Black Holes Milani, Farzad General Relativity and Quantum Cosmology High Energy Physics - Theory 83C57 . 83C75 . 83C45 . 81T20 Spacetime singularities represent a fundamental challenge in gravitational physics. We present a mathematically consistent framework for signature-changing black holes based on the $(2+1)$-dimensional BTZ metric, where the signature transitions from Lorentzian $(-,+,+)$ to Euclidean $(+,+,+)$ at the horizon. We identify and rectify a critical inconsistency in previous regularization schemes concerning second-order distributional terms $\varepsilon''(r)$, introducing a \emph{modified Hadamard regularization} that respects distribution theory. This produces a vacuum solution free of surface layers and impulsive gravitational waves. Geodesic analysis reveals that radially infalling observers require infinite proper time to reach the horizon, effectively preventing access to the would-be singularity while maintaining finite curvature invariants throughout the spacetime. We further establish the physical robustness of the geometry by demonstrating linear stability against gravitational perturbations, showing that quantum scalar field propagation remains unitary and well-defined across the signature change, and reinterpreting the $r=0$ region as a topological boundary rather than a curvature singularity. Our work establishes atemporality via signature change as a mathematically rigorous mechanism for \emph{singularity avoidance} in black hole spacetimes. |
| title | Consistent Regularization of Signature-Changing BTZ Black Holes |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory 83C57 . 83C75 . 83C45 . 81T20 |
| url | https://arxiv.org/abs/2512.01486 |