https://doi.org/10.1140/epjc/s10052-025-14879-3
Regular Article - Theoretical Physics
The shadow and quasinormal modes of the asymptotically flat hairy black holes with a dilaton potential
1
School of Science, Jiangsu University of Science and Technology, 212100, Zhenjiang, China
2
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
3
Institute of Physics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031, Lublin, Poland
Received:
7
August
2025
Accepted:
1
October
2025
Published online:
13
October
2025
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 
of the gravitational field, the mass M, the electric charge Q and the coupling constant 
between the U(1) field and the dilaton field, we find that the shadow radii, the Lyapunov exponent 
and the coordinate angular velocity 
only significantly affected by if the Q is close to the extremal value. Especially, near the 
critical point the phenomenon exhibits singular enhancement. Furthermore, the QNMs are numerically computed by using the Hatsuda method and verified with the higher-order WKB approximations with the Padé summation. We find that the QNMs are close to that of the low energy limit of the string theory when is large enough. In the eikonal limit, the real and imaginary parts are proved to be approximated by and , respectively.
© The Author(s) 2025
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