Can we know about black hole thermodynamics through shadows?

Understand

We investigate the relationship between shadow radius and microstructure for a general static spherically symmetric black hole and confirm their close connection.

• In this regard, we take the Reissner-Nordstr\"om (AdS) black hole as an example to do the concrete analysis.
• On the other hand, we study for the Kerr (AdS) black hole the relationship between its shadow and thermodynamics in the aspects of phase transition and microstructure.
• Our results for the Kerr (AdS) black hole show that the shadow radius $r_{\rm sh}$, the deformation parameters $\delta_s$ and $k_s$, and the circularity deviation $\Delta C$ can reflect the black hole thermodynamics.