Equatorial periodic orbits and gravitational wave signatures in Euler-Heisenberg black holes surrounded by perfect fluid dark matter

TL;DR

This paper studies equatorial periodic orbits and gravitational wave signatures around Euler-Heisenberg black holes with perfect fluid dark matter, revealing how quantum and dark matter effects influence orbital stability and waveforms.

Contribution

It introduces an effective metric incorporating quantum electrodynamic corrections and dark matter, analyzing geodesic dynamics, and computing gravitational wave signals in this modified spacetime.

Findings

Dark matter modifies stability thresholds and suppresses waveform amplitude.

QED corrections enhance high-frequency gravitational wave components.

Rich hierarchy of zoom-whirl motions observed in the strong-field regime.

Abstract

We investigate equatorial periodic orbits and their gravitational wave radiation in the spacetime of an Euler--Heisenberg (EH) black hole surrounded by perfect fluid dark matter (PFDM). The combined effects of quantum electrodynamic corrections and dark matter are incorporated through an effective metric, and the dynamics of timelike geodesics are analyzed using the effective potential formalism. We derive the conditions for marginally bound and innermost stable circular orbits, classify periodic trajectories using the rational parameter and topological indices, and identify a rich hierarchy of zoom--whirl motions in the strong-field regime. Gravitational wave signals from periodic orbits are computed using the numerical kludge method, revealing characteristic burst-like features associated with whirl phases. Our results show that perfect fluid dark matter systematically modifies the stability thresholds and suppresses the waveform amplitude, while QED corrections enhance high-frequency components generated near the horizon. These findings demonstrate that periodic orbits in the EH--PFDM spacetime provide a sensitive probe of quantum corrections and dark matter effects in strong gravitational fields.