Equatorial periodic orbits and gravitational waveforms in Bardeen black holes surrounded by perfect fluid dark matter

Abstract

To probe the interplay between dark matter (DM) and non-linear electrodynamics (NED), we consider the Bardeen black hole (BH) surrounded by perfect fluid dark matter (PFDM). We first compute the effective potential governing the particle trajectory, and then, by imposing suitable conditions on the potential, examine the effects of DM and NED on the marginally bound orbit (MBO) and innermost stable circular orbit (ISCO). In this study, we confine the particle's trajectory to the equatorial plane. We then investigate periodic orbits around the Bardeen BH surrounded by PFDM (BPFDM BH), considering the rational number $q$ associated with each periodic orbit. We use the $(z,w,v)$ taxonomy, which is widely used to systematically organize periodic orbits. We examine the variation of $q$ with energy and angular momentum, and also the variation of the angular momentum and energy required for a specific $(z,w,v)$ configuration with the magnetic charge $g$ and DM parameter $\b$. Finally, with the help of the numerical "Kludge" method, we examine gravitational waveforms emitted from EMRIs where the central supermassive BH is modeled as a BPFDM BH. Our study reveals distinct signatures of NED and DM on orbital dynamics and gravitational waveforms.