Gravitational wave signatures and periodic orbits of a charged black hole in a Hernquist dark matter halo

TL;DR

This paper investigates the motion of particles and gravitational wave signatures around a magnetically charged black hole within a Hernquist dark matter halo, highlighting how dark matter and magnetic charge influence orbital dynamics and gravitational wave polarization.

Contribution

It introduces a detailed analysis of periodic orbits and gravitational wave effects in a black hole-dark matter system with magnetic charge, extending previous models.

Findings

Dark matter parameters enlarge stable orbital regions.

Magnetic charge partially offsets dark matter effects.

Dark matter and magnetic charge influence gravitational wave polarizations.

Abstract

In this work, we study the motion of massive test particles and the gravitational--wave emission associated with periodic trajectories around a magnetically charged black hole immersed in a \textit{Hernquist} dark matter halo. We begin by analyzing the effective potential and the conditions for stable motion, with particular attention to the marginally bound radius and the innermost stable circular orbit. Our results show that the dark matter parameters, namely the halo density and scale radius, enlarge the allowed region and generally shift the relevant characteristic radii and angular momenta toward larger values. In contrast, the magnetic charge partially counterbalances this behavior. We then examine periodic trajectories through the rational number $q$, which characterizes the relation between the azimuthal and radial frequencies, and construct representative zoom--whirl configurations together with their precessing counterparts. Finally, we investigate the imprints of dark matter and magnetic monopole charge on the gravitational--wave polarizations in the extreme mass--ratio regime.