Analytical correspondence between shadow radius and black hole quasinormal frequencies

Understand

We consider the equivalence of quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope.

• Using WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and black hole shadow radius.
• We verify this correspondence with two black hole families in $4$ and $D$ dimensions, respectively.