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

TL;DR

This work analyzes high-dimensional static spherically symmetric black holes in Einstein-power-Yang-Mills-Gauss-Bonnet gravity, deriving a general shadow radius formula and a standardized high-dimensional constraint framework based on Schwarzschild-Tangherlini geometry. It shows that the Gauss-Bonnet coupling $\alpha_2$ predominantly governs both shadow properties and perturbation spectra, while the Yang-Mills charge $\mathcal{Q}$ and the power $q$ have negligible observable effects within the explored parameter space. The authors perform a thorough perturbation analysis for spin-0, spin-1, $p$-form, and spin-2 fields, employing WKB, AIM, and time-domain methods to compute QNMs and time-domain profiles, confirming cross-method consistency and identifying dimension-dependent stability bounds. The results demonstrate strong agreement between shadow-based constraints and dynamical stability analyses, reinforcing the validity of the proposed high-dimensional shadow constraint formula and its potential as a universal tool for constraining parameters of other high-dimensional black hole solutions.

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 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 $α_2$ 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 $α_2$ 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 conclusion of this cross-analysis further substantiate 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.

Figures (22)

• Figure 1: The schematic of the geometric projection of the photon's linear momentum $\boldsymbol{P}$ in the observer reference frame $\left\{ e_{\hat{r}}, \cdots, e_{{\hat{\theta}}_{\chi}}, \cdots, e_{{\hat{\theta}}_{n-2}} \right\}$. The vector $\vec{P}$ is represented as the $(n-1)$-vector $\boldsymbol{P}$. The symbol $r_{o}$ is the distance between the observer and the black hole, and $\theta_{o}$ is the inclination angle of the observer relative to the celestial plane.
• Figure 2: The blue-shaded region demarcates the admissible parameter space $\left({\alpha}_2, \mathcal{Q}\right)$ that ensures the existence of the event horizon in the special configuration of the EPYMGB black hole. The parameters $\mathsf{M}=1$ and $\mathscr{G}=1$ are selected.
• Figure 3: The red-shaded region demarcates the admissible parameter space $\left({\alpha}_2, \mathcal{Q}\right)$ that ensures the existence of the event horizon in the general configuration of the EPYMGB black hole. The parameters $\mathsf{M}=1$ and $\mathscr{G}=1$ are selected.
• Figure 4: The relevant parameters of the special configuration of the EPYMGB black hole are constrained through the high-dimensional shadow constraint formula \ref{['eq:highdimrange']}. The unfilled color region corresponds to the effective range $r_{\mathrm{sh}}$ of the shadow radius derived from the $\mathrm{M87}^{\star}$ observational data.
• Figure 5: Similar to Figure \ref{['figure4']}, but with the metric corresponding to the general configuration of the EPYMGB black hole.