Spin-($0$, $1$, $\frac{1}{2}$) Field Perturbations, Quasinormal Modes, Overtones, Greybody Factors and Strong Cosmic Censorship of Einstein-Skyrme Black Holes

We carry out a multi-spin perturbation-theory study of the four-dimensional Einstein-Skyrme (ES) anti-de Sitter (AdS) black hole (BH), whose lapse $f(r)=1-8\pi K-2M\mathrm{/}r+4\pi K\lambda \mathrm{/}{r}^2$ inherits two couplings from the hadronic model – the pion combination $K=F_{\pi }^2\mathrm{/}4$ and the Skyrme coupling $e$ – with $K\lambda =1\mathrm{/}{e}^2$ pinned by the theory rather than being a free integration constant. After deriving the Klein-Gordon, Maxwell and Dirac effective potentials on this background, we compute the quasinormal modes (QNMs) with the sixth-order WKB formula and cross-check them against the thirteenth-order Padé-improved expansion and the eikonal limit set by the unstable photon sphere. The first overtone $(n=1)$ of the scalar and electromagnetic channels reveals a mild Konoplya-Zhidenko anomaly: the ratio $\mathrm{\mid }\mathrm{I}\mathrm{m}{\omega }_1\mathrm{\mid }\mathrm{/}\mathrm{\mid }\mathrm{I}\mathrm{m}{\omega }_0\mathrm{\mid }$ drifts monotonically from $2.42$ to $2.54$, sitting noticeably below the Schwarzschild value near $3$. The dominant scalar mode is independently reproduced to better than $0.2\mathrm{\%}$ by a time-domain Prony fit. Greybody factors for all three spins follow the ordering $T_{\mathrm{E}\mathrm{M}}<T_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{r}}<T_{\mathrm{D}\mathrm{i}\mathrm{r}\mathrm{a}\mathrm{c}}$. Testing strong cosmic censorship at the Cauchy horizon, we find the Christodoulou parameter $\beta \lesssim 4\times {10}^{-3}$ across the admissible $(K,e)$ window – more than two orders of magnitude below the threshold $1\mathrm{/}2$ – with the margin protected by the theory itself.