Null geodesics, quasinormal modes, and thermodynamic phase transition for charged black holes in asymptotically flat and dS spacetimes

Understand

The numerical study indicates that there exists a relation between the quasinormal modes and the Davies point for a black hole.

• In this paper, we analytically study this relation for the charged Reissner-Nordstr\"{o}m black holes in asymptotically flat and dS spacetimes.
• In the eikonal limit, the angular velocity $\Omega$ and the Lyapunov exponent $\lambda$ of the photon sphere, respectively, corresponding to the real and imaginary parts of the quasinormal modes are obtained from the null geodesics.
• Both in asymptotically flat and dS spacetimes, we observe the spiral-like shapes in the complex quasinormal mode plane.