Standardized Constraints on the Shadow Radius and the Instability of Scalar, Electromagnetic, $p$-Form, and Gravitational Perturbations of High-Dimensional Spherically Symmetric Black Holes in Einstein-power-Yang-Mills-Gauss-Bonnet Gravity

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 of high-dimensional black holes by leveraging observational shadow data. 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 equations of motion and master variables 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 $\mathcal{Q}$ 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 ${\alpha }_2$ in various dimensions. Hence, the physical signatures of the parameters $\mathcal{Q}$ and $q$ in the black hole environment remain undetectable through either perturbation analysis or shadow observations. Cross-validation of the allowable range of ${\alpha }_2$ 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 conclusion of this cross-analysis further substantiates the accuracy of the high-dimensional shadow constraint formula proposed in this work, and we argue that this formula may serve as a universal tool for constraining the characteristic parameters of other high-dimensional spherically symmetric black hole solutions.