https://doi.org/10.1140/epjc/s10052-026-15344-5
Regular Article - Theoretical Physics
Periodic orbits and quasinormal modes of a black hole surrounded by King dark matter halo
1
Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia
2
Department of Physics and Electronics, Khazar University, 41 Mahsati Str, 1096, Baku, Azerbaijan
3
Purple Mountain Observatory, Chinese Academy of Sciences, 210023, Nanjing, China
4
Department of Physics, Madhabdev University, Narayanpur, 784164, Lakhimpur, Assam, India
5
Center for Theoretical Physics, Khazar University, 41 Mehseti Street, AZ1096, Baku, Azerbaijan
6
Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014, Helsinki, Finland
a
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Received:
2
November
2025
Accepted:
16
January
2026
Published online:
5
February
2026
Abstract
We examine the Hawking radiation sparsity and quasinormal mode (QNM) spectra of a Schwarzschild black hole surrounded by the King dark matter distribution. The modified metric, derived from the King density profile, yields altered expressions for the lapse function, mass, and Hawking temperature. The presence of dark matter reduces the Hawking temperature, indicating suppressed thermal emission. Analysis of radiation sparsity reveals its dependence on the horizon radius, with larger scale radius R and central density 
enhancing sparsity compared to the constant value in the Schwarzschild case. The photon sphere and shadow radius increase with R and , suggesting enlarged black hole shadows under dark matter influence. Hawking emission rates exhibit a downward shift in both peak intensity and frequency. The QNM spectra, obtained via the Mashhoon and 3rd-order Wentzel–Kramers–Brillouin (WKB) methods, show that both the oscillation frequencies and damping or decay rate decrease with the dark matter parameter 
. This study also examines how King dark matter halo affects periodic particle motion around a black hole, showing that it alters orbital stability and enhances precession, leading to transitions from bound to unbound motion. These results collectively demonstrate that King dark matter substantially modifies the thermodynamic and dynamical properties of black holes, offering potential observational imprints in black hole shadow and gravitational wave studies.
© The Author(s) 2026
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