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 $\mathcal{Q}$ 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 $\hat{I}{\pm }_2$ 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 $\hat{I}{\pm }_2$ 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.

72 pages, 22 figures, 4 tables