Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Universidad Nacional Autónoma de México
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G8716070160
OpenAlex ID: W7221112498