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arXiv · 2601.17613

From Thermodynamic Criticality to Geometric Criticality: A Linear Kernel Map from Matter Susceptibilities to Black-Hole Shadows

Jingxu Wu·Jie Shi·Chenjia Li·Yuwei Yin
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Abstract

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.

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Jingxu Wu, Jie Shi, Chenjia Li, Yuwei Yin. 2026-01-24. From Thermodynamic Criticality to Geometric Criticality: A Linear Kernel Map from Matter Susceptibilities to Black-Hole Shadows. https://arxiv.org/abs/2601.17613

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