Observational signatures of charged Bardeen black holes in perfect fluid dark matter with a cloud of strings

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.

💡 Research Summary

The paper presents a new static, spherically symmetric black‑hole solution that simultaneously incorporates three distinct physical ingredients: (i) a magnetic monopole charge arising from nonlinear electrodynamics (NED) that regularizes the central singularity in the spirit of the Bardeen model, (ii) a surrounding perfect‑fluid dark‑matter (PFDM) halo that contributes a logarithmic term to the metric, and (iii) a cloud of strings (CS) that introduces a constant deficit parameter α, making the spacetime asymptotically non‑flat. Starting from the action S = ∫√−g(R + L(NED) + L_EM) + S_DM + S_CS, the authors derive the field equations and obtain the metric function

f(r)=1−α−2M r²/(q²+r²)^{3/2}+Q²/r²+β r ln(r/|β|),

where M is the black‑hole mass, q the magnetic charge, Q the electric charge, α∈