Optical appearance, Hawking radiation, and Barrow thermodynamics of Letelier black hole in electromagnetic universe

Abstract: We present an investigation of a static, spherically symmetric Letelier black hole (BH) immersed in an electromagnetic universe (EMU), characterized by the cloud of strings (CoS) parameter $α$ and the EMU parameter $a$. The photon sphere and shadow radius are derived analytically, revealing how both parameters modify the apparent BH silhouette compared to the Schwarzschild case. We extend the shadow analysis to homogeneous and inhomogeneous plasma environments, demonstrating systematic reductions in the observed shadow size, and compute the weak gravitational lensing deflection angle in plasma using the Gauss-Bonnet theorem. The perturbative dynamics are investigated for scalar, electromagnetic, and Dirac fields, with quasinormal mode frequencies obtained via the sixth-order WKB approximation and greybody factors calculated using the rigorous bounds method. The resulting Hawking radiation spectra reveal distinct signatures for bosonic and fermionic emission channels. We further analyze quasi-periodic oscillations by deriving the fundamental orbital frequencies and applying both parametric resonance and relativistic precession models, obtaining constraints from observations.