https://doi.org/10.1140/epjc/s10052-026-15293-z
Regular Article - Theoretical Physics
Shadow and quasi-normal modes of Schwarzschild–Hernquist black hole
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 300350, Tianjin, China
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
16
September
2025
Accepted:
3
January
2026
Published online:
19
January
2026
Abstract
In this paper we study the shadow and quasi-normal modes (QNMs) of a black hole (BH) surrounded by a dark matter halo with Hernquist-type density distribution, which was reported in Cardoso et al. (Phys. Rev. D 105(6):L061501, 2022). In astrophysical scenarios, we find that the shadow radius enlarges as the compactness of halo increases. Therefore, we obtain an upper bound for the compactness 
with the Event Horizon Telescope (EHT) observations. We calculate axial gravitational QNMs of the galactic BH up to 
, and fit the redshift relative to Schwarzschild QNMs up to second order in the compactness (for 
. These highly redshifted QNMs, resulting from large compactness, are key to modeling the dark matter halo.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
