From Thermodynamic Criticality to Geometric Criticality: A Linear Kernel Map from Matter Susceptibilities to Black-Hole Shadows
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918303756189696 |
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| author | Wu, Jingxu Shi, Jie Li, Chenjia Yin, Yuwei |
| author_facet | Wu, Jingxu Shi, Jie Li, Chenjia Yin, Yuwei |
| contents | We construct an explicit linear map from compact, conserved thermodynamic/effective-medium perturbations of the stress-energy tensor to the metric response in static, spherically symmetric spacetimes, and from there to geometric observables of direct relevance to horizon-scale imaging: the shadow radius and photon-sphere frequency. The response is expressed through $L^{1}$-bounded kernels written in a piecewise "local $+$ tail" form, which makes transparent the separation between near-photon-sphere sensitivity and far-zone contributions (including AdS tails). Under mild assumptions on the matter susceptibilities near a critical point, dominated convergence transfers the thermodynamic exponent to the geometric susceptibility, $γ_{\rm sh}=γ_{\rm th}$, with controlled analytic corrections. We further provide AdS far-zone bounds with explicit outside-support constants depending only on background geometric data at the photon sphere and shell geometry. A reproducible numerical pipeline with convergence diagnostics is presented and benchmarked. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17613 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Thermodynamic Criticality to Geometric Criticality: A Linear Kernel Map from Matter Susceptibilities to Black-Hole Shadows Wu, Jingxu Shi, Jie Li, Chenjia Yin, Yuwei General Relativity and Quantum Cosmology High Energy Physics - Theory We construct an explicit linear map from compact, conserved thermodynamic/effective-medium perturbations of the stress-energy tensor to the metric response in static, spherically symmetric spacetimes, and from there to geometric observables of direct relevance to horizon-scale imaging: the shadow radius and photon-sphere frequency. The response is expressed through $L^{1}$-bounded kernels written in a piecewise "local $+$ tail" form, which makes transparent the separation between near-photon-sphere sensitivity and far-zone contributions (including AdS tails). Under mild assumptions on the matter susceptibilities near a critical point, dominated convergence transfers the thermodynamic exponent to the geometric susceptibility, $γ_{\rm sh}=γ_{\rm th}$, with controlled analytic corrections. We further provide AdS far-zone bounds with explicit outside-support constants depending only on background geometric data at the photon sphere and shell geometry. A reproducible numerical pipeline with convergence diagnostics is presented and benchmarked. |
| title | From Thermodynamic Criticality to Geometric Criticality: A Linear Kernel Map from Matter Susceptibilities to Black-Hole Shadows |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.17613 |