Signatures of a Schwarzschild-like Black Hole Immersed in Dark Matter Halo

TL;DR

This work investigates a Schwarzschild-like black hole embedded in a Dehnen-type dark matter halo, characterized by $(\alpha,\beta,\gamma)=(1,4,2)$, and analyzes scalar, electromagnetic, and axial gravitational perturbations. Using sixth- and eighth-order WKB methods with Padé resummation, it computes quasinormal modes and shows that increasing halo density $\rho_s$ and scale $r_s$ decreases both the oscillation frequency $\Re(\omega)$ and damping $|\Im(\omega)|$, implying longer-lived modes. Geodesic analysis coupled with the EHT shadow constraint for Sgr A$^*$ bounds the halo parameters via the shadow radius $R_{\rm sh}$, while greybody factors computed from WKB indicate enhanced transmission through the halo-modified potential barrier across spins. The combined results reveal measurable imprints of the dark-matter environment on black hole oscillations and Hawking-radiation signatures, offering potential observational avenues for future gravitational-wave and black-hole-imaging studies. The paper also outlines future extensions to fermionic perturbations, polar-sector analyses, and time-domain evolution to further probe the DM–BH interplay.

Abstract

Astrophysical black holes are often surrounded by dark matter, which can influence their dynamics and observational signatures. In this work, we study a Schwarzschild-like black hole immersed in a Dehnen-type $(1,4,2)$ dark matter halo and analyse scalar, electromagnetic, and gravitational perturbations in this spacetime. We compute quasinormal modes (QNMs) using the Wentzel-Kramers-Brillouin (WKB) approximation method with Padé approximants, investigate particle motion and photon trajectories, and use black hole shadow observations to place constraints on the halo parameters. We further examine the greybody factors associated with Hawking radiation for different perturbation spins. This combined analysis aims to understand how dark matter environments may affect black hole oscillations, radiation properties, and the corresponding observational signatures.

Figures (5)

• Figure 1: Variation of $f(r)$ with respect to the radial distance for various values of $\rho_{s} = 0.00$ (Blue), 0.01 (Red), 0.03 (Green) and 0.06 (Orange), we set M = 1 and $r_{s} = 0.8$.
• Figure 2: Variation of $f(r)$ with respect to the radial distance for various values of $r_{s} = 0.00$ (Blue), 0.04 (Red), 0.65 (Green) and 0.8 (Orange), we set M = 1 and $\rho_{s} = 0.06$
• Figure 4: Allowed parameter space for the halo density $\rho_s$ and scale radius $r_s$ obtained from the Sgr A$^*$ shadow measurement. The dashed contour denotes the maximum shadow radius of $5.22$, and all points lying below this boundary in the blue shaded region satisfy the observational constraint.
• Figure 5: Greybody factors $|\Gamma_{\ell}(\omega)|^2$ for scalar field perturbations in the Schwarzschild-like black hole surrounded by a Dehnen-type dark-matter halo. The left panel corresponds to the parameters $\rho_s = 0.02$ and $r_s = 0.25$, while the right panel shows the case $\rho_s = 0.07$ and $r_s = 0.8$ with $l = 2$ (blue), $l =3$ (green), $l=4$ (red), $l=5$ (orange).
• Figure : Effective potential $V(r)$ versus tortoise coordinate $r_\ast$ for scalar field perturbations. Left: fixed $r_s = 0.7$ with varying $\rho_s$; Right: fixed $\rho_s = 0.06$ with varying $r_s$.