Quasinormal Modes and Neutrino Energy Deposition for a Magnetically Charged Black Hole in a Hernquist Dark Matter Halo

TL;DR

This paper studies how a magnetically charged black hole in a dark matter halo affects quasinormal modes, shadow, lensing, and neutrino annihilation, revealing the interplay between magnetic charge and dark matter environment.

Contribution

It provides a comprehensive analysis of the combined effects of magnetic charge and dark matter halo on black hole observables and neutrino processes, using analytic and numerical methods.

Findings

Magnetic charge increases oscillation frequency and damping rate.

Dark matter halo shifts quasinormal spectrum in the opposite direction.

Halo and magnetic effects partially cancel in certain modes.

Abstract

We investigate quasinormal modes, shadow observables, weak gravitational lensing, and neutrino--antineutrino annihilation for a static, spherically symmetric black hole that carries a nonlinear-electrodynamics magnetic charge and is embedded in a Hernquist dark-matter halo. The geometry is controlled by the black-hole mass $M$, magnetic charge $g$, and halo parameters $(\alpha,\beta)$, and provides a simple analytic setting in which compact-object and environmental deformations can be studied simultaneously. We derive the scalar, electromagnetic, and axial gravitational master equations and compute the corresponding quasinormal spectra using a high-order WKB expansion supplemented by Pade resummation. The magnetic charge raises the real oscillation frequency and slightly increases the damping rate, whereas the Hernquist halo shifts the spectrum in the opposite direction; for suitable parameters the two effects partially cancel at the level of individual modes. We then connect the eikonal spectrum with the photon sphere and shadow radius, emphasizing the distinction between comparisons performed at fixed bare mass and at fixed asymptotic mass $\mathcal{M}=M+\alpha$. At fixed asymptotic mass, the residual NED and halo-concentration terms reduce the shadow and the weak-deflection angle relative to Schwarzschild at the first nontrivial order. Finally, we formulate neutrino-pair annihilation in the same background, including the angular factor, Tolman-redshifted $T^9$ kernel, integrated deposition rate, and reduced shell profile. The magnetic sector suppresses the annihilation efficiency, while the halo sector enhances it through its lowering of the lapse. These results show that ringdown, imaging, lensing, and high-energy deposition probe the same underlying competition between near-horizon magnetic structure and extended dark-matter environment, but with different parameter weights.