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

Spin-($0$, $1$, $frac{1}{2}$) Field Perturbations, Quasinormal Modes, Overtones, Greybody Factors and Strong Cosmic Censorship of Einstein-Skyrme Black Holes
Faizuddin Ahmed, Ahmad Al-Badawi, .Izzet Sakall{i}
arXiv:2604.09740v1 Announce Type: cross
Abstract: 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 $f(r)=1-8pi K-2M/r+4pi Klambda/r^{2}$ inherits two couplings from the hadronic model — the pion combination $K=F_{pi}^{2}/4$ and the Skyrme coupling $e$ — with $Klambda=1/e^{2}$ 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 Pad’e-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 $|mathrm{Im},omega_{1}|/|mathrm{Im},omega_{0}|$ 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 $0.2%$ by a time-domain Prony fit. Greybody factors for all three spins follow the ordering $T_{rm EM}arXiv:2604.09740v1 Announce Type: cross
Abstract: 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 $f(r)=1-8pi K-2M/r+4pi Klambda/r^{2}$ inherits two couplings from the hadronic model — the pion combination $K=F_{pi}^{2}/4$ and the Skyrme coupling $e$ — with $Klambda=1/e^{2}$ 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 Pad’e-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 $|mathrm{Im},omega_{1}|/|mathrm{Im},omega_{0}|$ 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 $0.2%$ by a time-domain Prony fit. Greybody factors for all three spins follow the ordering $T_{rm EM}