Zero-point length as a topological protection of black hole regularity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866918367201329152 |
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| author | Anand, Ankit Jusufi, Kimet Bambi, Cosimo |
| author_facet | Anand, Ankit Jusufi, Kimet Bambi, Cosimo |
| contents | We investigate the thermodynamic topology of regular black holes with zero-point length using an extended first law that includes the zero-point length stored in the geometry. By treating the regularization scale $l_0$ as a thermodynamic variable, we analyze the Hessian geometry of the thermodynamic manifold and demonstrate that the vector field $\vecϕ = (T, Ψ)$, where $T$ is the temperature and $Ψ$ is the conjugate to $l_0$, never vanishes in the physical parameter space for $l_0 > 0$. This implies the absence of Morse critical points and a vanishing winding number ($W = 0$), indicating topological protection against the formation of naked singularities. Crucially, we show that in the singular limit $l_0 \to 0$, a non-zero winding number ($W = 1$) emerges, characterizing the Schwarzschild singularity as a topological defect. The conservation of this topological invariant under smooth evolution provides a rigorous topological formulation of the weak cosmic censorship conjecture: the presence of zero-point length not only regularizes the spacetime background but also enforces topological protection against the formation of singularities, preventing black hole-to-naked singularity transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02295 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zero-point length as a topological protection of black hole regularity Anand, Ankit Jusufi, Kimet Bambi, Cosimo General Relativity and Quantum Cosmology High Energy Physics - Theory We investigate the thermodynamic topology of regular black holes with zero-point length using an extended first law that includes the zero-point length stored in the geometry. By treating the regularization scale $l_0$ as a thermodynamic variable, we analyze the Hessian geometry of the thermodynamic manifold and demonstrate that the vector field $\vecϕ = (T, Ψ)$, where $T$ is the temperature and $Ψ$ is the conjugate to $l_0$, never vanishes in the physical parameter space for $l_0 > 0$. This implies the absence of Morse critical points and a vanishing winding number ($W = 0$), indicating topological protection against the formation of naked singularities. Crucially, we show that in the singular limit $l_0 \to 0$, a non-zero winding number ($W = 1$) emerges, characterizing the Schwarzschild singularity as a topological defect. The conservation of this topological invariant under smooth evolution provides a rigorous topological formulation of the weak cosmic censorship conjecture: the presence of zero-point length not only regularizes the spacetime background but also enforces topological protection against the formation of singularities, preventing black hole-to-naked singularity transitions. |
| title | Zero-point length as a topological protection of black hole regularity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.02295 |