Quasinormal ringing of a regular black hole sourced by the Dehnen-type distribution of matter

TL;DR

This paper investigates the quasinormal modes of a regular black hole influenced by a Dehnen-type matter distribution, finding that dark matter halos cause minimal deviations in black hole oscillation spectra.

Contribution

It provides the first detailed analysis of quasinormal modes for a regular black hole with a Dehnen matter distribution, demonstrating stability and quantifying dark matter effects.

Findings

Quasinormal frequencies are stable and computed with high accuracy.

Dark matter halos cause small changes in oscillation frequencies.

Deviations from Schwarzschild are negligible for realistic dark matter densities.

Abstract

We study quasinormal modes of test scalar, electromagnetic, and Dirac fields in the background of a new analytic regular black-hole solution obtained as an exact solution of the Einstein equations sourced by a Dehnen-type matter distribution in [R. A. Konoplya, A. Zhidenko, arXiv:2511.03066]. The metric is asymptotically flat and characterized by a simple lapse function $f(r)=1-2 M r^{2}/(r+a)^{3}$, where $M$ is the ADM mass and $a$ represents the characteristic scale of the surrounding dark-matter halo that regularizes the central region. The effective potentials for all perturbing fields possess the standard single-barrier form, ensuring linear stability and the applicability of the WKB formalism. The quasinormal frequencies are computed using the sixth- and ninth-order WKB methods with Pad\'e corrections and verified by time-domain integration, both approaches showing excellent agreement. The parameter $a$ leads to a moderate increase in the real oscillation frequency, while the damping rate remains almost unchanged, producing only small corrections to the Schwarzschild spectrum. Since such deviations become appreciable only for unrealistically dense halos, our results confirm that the quasinormal spectrum of astrophysical black holes is safely unaffected by ordinary galactic dark-matter environments.