The connection between the shadow radius and the Ruppeiner geometry of a charged static spherically symmetric black hole is investigated. The normalized curvature scalar is adopted, and its close relation to the Van der Waals-like and Hawking-Page phase transition of Reissner-Nordstr\"{o}m AdS black hole is studied. The results show that the shadow radius is a useful tool to reveal the correct information of the phase structure and the underlying microstructure of the black hole, which opens a new window to investigate the strong gravity system from the observational point of view.
@article{arxiv.2107.12615,
title = {Ruppeiner Geometry of the RN-AdS Black Hole Using Shadow Formalism},
author = {Chao Wang and Bin Wu and Zhen-Ming Xu and Wen-Li Yang},
journal= {arXiv preprint arXiv:2107.12615},
year = {2022}
}