Black Hole Shadows and Quasinormal Modes with Dark Matter at the Horizon
Abstract
In this work, we study the effect of a surrounding dark matter halo on two horizon-scale observables of a black hole: its shadow and quasinormal-mode spectrum. We consider a Schwarzschild black hole embedded in a Hernquist halo and construct a one-parameter family of solutions that preserve the total halo mass while varying how the halo density vanishes at the horizon. By closing the Einstein equations with an Einstein-cluster stress tensor, we show that horizon regularity requires the density to vanish at least linearly. Our results also indicate that the dominant energy condition is violated in a thin layer outside the horizon, highlighting the limitations of the Einstein-cluster description within the photon sphere. We demonstrate that, at fixed black hole mass, the halo always enlarges the shadow, with the effect becoming more pronounced for more massive and compact halos. Comparison with Event Horizon Telescope observations of Sgr\,A* and M87* shows that only sufficiently compact halos can be constrained, with the inferred bounds depending sensitively on whether the observed mass is identified with the black hole mass or the total mass of the system. We further show that the halo lowers both the oscillation frequencies and damping rates of electromagnetic and axial gravitational quasinormal modes, leading to higher quality factors. These spectral shifts are quantitatively explained by changes in the photon-sphere properties through the eikonal correspondence. Since the effects scale with the ratio of the halo mass to its size, they are observable only for dark matter concentrated within a few tens of gravitational radii of the black hole, which is the regime considered here.
Related
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- Long-lived quasinormal modes, shadows and particle motion in four-dimensional quasi-topological gravity
BibTeX
@misc{sadeghi2026black,
title = {{Black Hole Shadows and Quasinormal Modes with Dark Matter at the Horizon}},
author = {Armin Sadeghi and Javad T. Firouzjaee and Saeed Fakhry},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30312},
eprint = {2610.30312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30312},
}
RIS
TY - UNPB
TI - Black Hole Shadows and Quasinormal Modes with Dark Matter at the Horizon
AU - Armin Sadeghi
AU - Javad T. Firouzjaee
AU - Saeed Fakhry
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30312
UR - https://arxiv.org/abs/2610.30312
AB - In this work, we study the effect of a surrounding dark matter halo on two horizon-scale observables of a black hole: its shadow and quasinormal-mode spectrum. We consider a Schwarzschild black hole embedded in a Hernquist halo and construct a one-parameter family of solutions that preserve the total halo mass while varying how the halo density vanishes at the horizon. By closing the Einstein equations with an Einstein-cluster stress tensor, we show that horizon regularity requires the density to vanish at least linearly. Our results also indicate that the dominant energy condition is violated in a thin layer outside the horizon, highlighting the limitations of the Einstein-cluster description within the photon sphere. We demonstrate that, at fixed black hole mass, the halo always enlarges the shadow, with the effect becoming more pronounced for more massive and compact halos. Comparison with Event Horizon Telescope observations of Sgr\,A^* and M87^* shows that only sufficiently compact halos can be constrained, with the inferred bounds depending sensitively on whether the observed mass is identified with the black hole mass or the total mass of the system. We further show that the halo lowers both the oscillation frequencies and damping rates of electromagnetic and axial gravitational quasinormal modes, leading to higher quality factors. These spectral shifts are quantitatively explained by changes in the photon-sphere properties through the eikonal correspondence. Since the effects scale with the ratio of the halo mass to its size, they are observable only for dark matter concentrated within a few tens of gravitational radii of the black hole, which is the regime considered here.
ER -