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arXiv · 2610.10638

Geometrothermodynamics of Black Hole Shadows: A Review

Hernando Quevedo·Jose M. Ladino·Carlos E. Romero-Figueroa·Sasha A. Zaldivar
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Abstract

Black-hole shadows and geometrothermodynamics (GTD) are defined in different spaces but depend on the same macroscopic black-hole parameters. We review their correspondence for Reissner--Nordström (RN), Kerr, and Kerr--AdS black holes. The three GTD metrics reveal complementary thermodynamic structures, including Davies instabilities, extremal and degenerate limits, and regular curvature zeros, which can be mapped to shadow configurations. Kerr--AdS extends this correspondence to asymmetric shadows and multidimensional equilibrium states. We formulate a local Jacobian-rank criterion for thermodynamic reconstruction from shadow observables and discuss shadow--microstructure (SM) diagrams as optical representations of GTD-classified equilibrium states. The application to Sagittarius A* illustrates the inverse problem: shadow observations constrain thermodynamic states and provide a basis for identifying additional metric-dependent observables that could distinguish among the GTD metric structures.

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Hernando Quevedo, Jose M. Ladino, Carlos E. Romero-Figueroa, Sasha A. Zaldivar. 2026-10-07. Geometrothermodynamics of Black Hole Shadows: A Review. https://arxiv.org/abs/2610.10638

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