Geometrothermodynamics of Black Hole Shadows: A Review

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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BibTeX

@misc{quevedo2026geometrothermodynamics,
  title = {{Geometrothermodynamics of Black Hole Shadows: A Review}},
  author = {Hernando Quevedo and Jose M. Ladino and Carlos E. Romero-Figueroa and Sasha A. Zaldivar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10638},
  eprint = {2610.10638},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10638},
}

RIS

TY  - UNPB
TI  - Geometrothermodynamics of Black Hole Shadows: A Review
AU  - Hernando Quevedo
AU  - Jose M. Ladino
AU  - Carlos E. Romero-Figueroa
AU  - Sasha A. Zaldivar
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10638
UR  - https://arxiv.org/abs/2610.10638
AB  - 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.
ER  -

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