Probing Lorentz symmetry violation and topological defects in Euler-Heisenberg black hole through shadows, scalar perturbations, and thermodynamics

In this work, we study a charged black hole incorporating Euler-Heisenberg nonlinear electrodynamics, a global monopole, and spontaneous Lorentz-symmetry breaking generated by a Kalb-Ramond tensor field. We analyze the effects of the model parameters on the spacetime geometry, photon sphere, black-hole shadow, scalar perturbations, and thermodynamic properties. The results show that the nonlinear electromagnetic coupling, the monopole parameter, and the Lorentz-violating sector significantly modify the horizon structure, effective potentials, and shadow observables. Furthermore, the thermodynamic analysis reveals critical behavior associated with heat-capacity divergences, indicating second-order phase transitions and nontrivial stability regions. Our findings demonstrate that the combined effects of nonlinear electrodynamics, topological defects, and Lorentz-symmetry violation produce measurable deviations from standard charged black-hole solutions and enrich both their optical and thermodynamic properties.