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From Thermodynamic Criticality to Geometric Criticality: A Linear Kernel Map from Matter Susceptibilities to Black-Hole Shadowsстатья
- Авторы: Wu Jingxu, Shi Jie, Li Chenjia, Yin Yuwei
- Журнал: ArXiv e-prints
- Год издания: 2026
- DOI: 10.48550/arXiv.2601.17613
- Аннотация: 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, \gamma_{\rm sh}=\gamma_{\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.
- Добавил в систему: У Цзинсюй