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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2604.28050 |
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| _version_ | 1866917451290116096 |
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| author | Joshi, Sudhanva Mishra, Sunil Kumar |
| author_facet | Joshi, Sudhanva Mishra, Sunil Kumar |
| contents | The black hole no-hair theorem is traditionally derived from the uniqueness theorems of general relativity. We show that a quantitative form follows from unitarity together with the standard semiclassical assumptions of horizon causality and interior accessibility. For a semiclassical black hole, we prove that the trace distance between exterior states corresponding to two same-charge infalling states is bounded by $2\sqrt{2\varepsilon}$, where $\varepsilon$ quantifies the diamond norm departure of the interior channel from a perfect isometry which is a quantitative measure of horizon-smoothness violation that upper-bounds $1 - F_I$, where $F_I$ is the interior fidelity capturing how faithfully the infalling state is retained. Inverting this relation yields a trade-off inequality, $\varepsilon \geq D_{\max}^2/8$, between the maximum exterior distinguishability $D_{\max}$ and the degree of horizon smoothness. This establishes that observable exterior quantum hair is quantitatively incompatible with exact horizon smoothness under unitary evolution: any model predicting nonzero exterior hair must violate the equivalence principle at the horizon by a quantifiable amount. Pre-existing entanglement with the infalling system is the only channel for quantum hair compatible with both unitarity and horizon smoothness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_28050 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A No-Cloning Trade-off Between Black Hole No-Hair and Horizon Smoothness Joshi, Sudhanva Mishra, Sunil Kumar Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory The black hole no-hair theorem is traditionally derived from the uniqueness theorems of general relativity. We show that a quantitative form follows from unitarity together with the standard semiclassical assumptions of horizon causality and interior accessibility. For a semiclassical black hole, we prove that the trace distance between exterior states corresponding to two same-charge infalling states is bounded by $2\sqrt{2\varepsilon}$, where $\varepsilon$ quantifies the diamond norm departure of the interior channel from a perfect isometry which is a quantitative measure of horizon-smoothness violation that upper-bounds $1 - F_I$, where $F_I$ is the interior fidelity capturing how faithfully the infalling state is retained. Inverting this relation yields a trade-off inequality, $\varepsilon \geq D_{\max}^2/8$, between the maximum exterior distinguishability $D_{\max}$ and the degree of horizon smoothness. This establishes that observable exterior quantum hair is quantitatively incompatible with exact horizon smoothness under unitary evolution: any model predicting nonzero exterior hair must violate the equivalence principle at the horizon by a quantifiable amount. Pre-existing entanglement with the infalling system is the only channel for quantum hair compatible with both unitarity and horizon smoothness. |
| title | A No-Cloning Trade-off Between Black Hole No-Hair and Horizon Smoothness |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.28050 |