Spin-($0$, $1$, $\frac{1}{2}$) Field Perturbations, Quasinormal Modes, Overtones, Greybody Factors and Strong Cosmic Censorship of Einstein-Skyrme Black Holes
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| Format: | Preprint |
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2026
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| _version_ | 1866917400060887040 |
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| author | Ahmed, Faizuddin Al-Badawi, Ahmad Sakallı, İzzet |
| author_facet | Ahmed, Faizuddin Al-Badawi, Ahmad Sakallı, İzzet |
| contents | 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 $f(r)=1-8πK-2M/r+4πKλ/r^{2}$ inherits two couplings from the hadronic model -- the pion combination $K=F_π^{2}/4$ and the Skyrme coupling $e$ -- with $Kλ=1/e^{2}$ 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 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 $|\mathrm{Im}\,ω_{1}|/|\mathrm{Im}\,ω_{0}|$ 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 $T_{\rm EM}<T_{\rm scalar}<T_{\rm Dirac}$. Testing strong cosmic censorship at the Cauchy horizon, we find the Christodoulou parameter $β\lesssim 4\times 10^{-3}$ across the admissible $(K,e)$ window -- more than two orders of magnitude below the threshold $1/2$ -- with the margin protected by the theory itself. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_09740 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spin-($0$, $1$, $\frac{1}{2}$) Field Perturbations, Quasinormal Modes, Overtones, Greybody Factors and Strong Cosmic Censorship of Einstein-Skyrme Black Holes Ahmed, Faizuddin Al-Badawi, Ahmad Sakallı, İzzet General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory 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 $f(r)=1-8πK-2M/r+4πKλ/r^{2}$ inherits two couplings from the hadronic model -- the pion combination $K=F_π^{2}/4$ and the Skyrme coupling $e$ -- with $Kλ=1/e^{2}$ 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 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 $|\mathrm{Im}\,ω_{1}|/|\mathrm{Im}\,ω_{0}|$ 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 $T_{\rm EM}<T_{\rm scalar}<T_{\rm Dirac}$. Testing strong cosmic censorship at the Cauchy horizon, we find the Christodoulou parameter $β\lesssim 4\times 10^{-3}$ across the admissible $(K,e)$ window -- more than two orders of magnitude below the threshold $1/2$ -- with the margin protected by the theory itself. |
| title | Spin-($0$, $1$, $\frac{1}{2}$) Field Perturbations, Quasinormal Modes, Overtones, Greybody Factors and Strong Cosmic Censorship of Einstein-Skyrme Black Holes |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.09740 |