Probing the Charged Hayward Black Hole in Dark Matter and String Cloud Environments through Shadow, Geodesics, and Quasinormal Spectrum

Abstract: We construct a charged Bardeen black hole (BH) surrounded by perfect fluid dark matter (PFDM) and coupled to a cloud of strings (CS). The metric function combines the magnetic monopole charge from nonlinear electrodynamics, the PFDM logarithmic correction, and the CS parameter that renders the spacetime asymptotically non-flat. We analyze the horizon structure, identifying parameter ranges yielding non-extremal BHs, extremal configurations, and naked singularities. The null geodesics, photon sphere radius, and shadow are computed, revealing that both CS and PFDM enlarge the shadow. For neutral particle dynamics, we derive the specific energy, angular momentum, and innermost stable circular orbit location. Quasiperiodic oscillations (QPOs) are examined through the azimuthal, radial, and vertical epicyclic frequencies, where notably the azimuthal frequency is independent of the CS parameter. Scalar field perturbations governed by the Klein-Gordon equation yield an effective potential whose peak decreases with both parameters, yet the transmission and reflection probabilities respond oppositely to CS and PFDM variations. The greybody factor bounds are obtained using semi-analytical methods. Our results demonstrate that the distinct effects of $α$ and $β$ on various observables could allow independent constraints on these parameters through shadow measurements, QPO timing, and gravitational wave ringdown observations.