The shadow and quasinormal modes of the asymptotically flat hairy black holes with a dilaton potential

TL;DR

This paper investigates the shadow and quasinormal modes of a specific class of asymptotically flat hairy black holes with a dilaton potential, revealing how these properties depend on parameters like charge and coupling constant.

Contribution

It provides a detailed analysis of black hole shadows and QNMs in a dilaton black hole solution, including numerical computations and their relation to string theory limits.

Findings

Shadow radii and QNMs are significantly affected by the coupling constant when charge is near extremal.

QNMs match the low energy string theory limit for large coupling constant.

In the eikonal limit, QNM frequencies relate directly to shadow properties.

Abstract

In this article, the shadow and the quasinormal modes (QNMs) of an exact asymptotically flat hairy electrically charged black hole solution with a dilaton potential are investigated. Using the {constraint} equation among the integration constant $\eta$ of the gravitational field, the mass $M$, the electric charge $Q$ and the coupling constant $\nu$ between the $U(1)$ field and the dilaton field, we find that the shadow radii, the Lyapunov exponent $\lambda$ and the coordinate angular velocity $\Omega_{c}$ only significantly affected by $\nu$ if the $Q$ is close to the extremal value, especially when $\nu$ approaches to one. Furthermore, the QNMs are numerically computed by using the Hatsuda method and verify with the higher-order WKB approximations with the Pad\'e summation. We find that the QNMs are close to that of the low energy limit of the string theory when $\nu$ is large enough. In the eikonal limit, the real and imaginary parts are proved to be given by $\Omega_{c}$ and $\lambda$, respectively.