Long-lived quasinormal modes and grey-body factors of supermassive black holes with a dark matter halo

TL;DR

This study analyzes how a dark matter halo influences the quasinormal modes and grey-body factors of a black hole, finding minimal impact for realistic halo parameters and longer-lived oscillations with increasing scalar field mass.

Contribution

It provides the first detailed computation of quasinormal modes and grey-body factors for black holes with a dark matter halo using high-order WKB methods and time-domain analysis.

Findings

Real part of frequency slightly increases with field mass

Damping rate decreases with field mass, leading to longer-lived modes

Dark matter halo parameters have negligible effect on ringdown signatures

Abstract

We study quasinormal modes and grey-body factors of a massive scalar field in the background of a Schwarzschild black hole surrounded by a spherically symmetric galactic dark matter halo. The background metric, recently obtained as an analytic generalization of the Schwarzschild geometry, depends on the halo velocity parameter $V_{c}$ and the core radius $a$. Using the sixth- and seventh-order WKB methods with Pade approximants, supported by time-domain integration and Prony analysis, we compute the fundamental quasinormal frequencies and transmission coefficients. The results show that the real part of the frequency slightly increases while the damping rate decreases with growing field mass $\mu$, leading to longer-lived oscillations. The influence of the dark matter halo parameters is found to be negligible for astrophysically realistic values, confirming the robustness of Schwarzschild-like ringdown signatures. Grey-body factors decrease with increasing field mass and multipole number, while the effect of the halo parameters remains small.