Constraints on shadow radius and instabilities arising from various perturbations in spherically symmetric black holes in Einstein–power–Yang–Mills–Gauss–Bonnet gravity

Abstract The space-time geometry under investigation is chosen to be a high-dimensional, static, spherically symmetric solution in an asymptotically flat background within the Einstein–power–Yang–Mills–Gauss–Bonnet (EPYMGB) gravity. To address the limitations of previous shadow constraints, we construct a standardized framework based on the Schwarzschild-Tangherlini metric to constrain the characteristic parameters. Additionally, we provide a rigorous derivation of the shadow radius formula for a general high-dimensional spherically symmetric black hole. Subsequently, we systematically and comprehensively present the effective potential equations governing spin-0, spin-1, p -form, and spin-2 perturbations in high-dimensional static spherically symmetric flat space-time. Our analysis reveals that the Yang–Mills magnetic charge $$\mathcal {Q}$$ Q and the power q have a negligible impact on both the shadow radius and perturbations of the black hole when compared to the Gauss–Bonnet coupling constant $${\alpha }_2$$ α 2 in various dimensions. Hence, the physical signatures of the parameters $$\mathcal {Q}$$ Q and q in the black hole environment remain undetectable through either perturbation analysis or shadow observations. Cross-validation of the allowable range of $${\alpha }_2$$ α 2 derived from the high-dimensional constraint on shadow radius and the dynamical stability analysis of gravitational perturbations demonstrates excellent agreement between these independent approaches. The conclusions derived from the cross-analysis further substantiate the validity of the high-dimensional shadow constraint formula proposed in this work and indicate that the duality between black hole shadows and perturbations may persist in high-dimensional space-times.