史瓦西背景下洛伦兹破缺Kalb-Ramond场的零模与振荡不稳定性
Zero modes and oscillatory instabilities of a Lorentz-violating Kalb-Ramond field on a Schwarzschild background
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中文总结 AI 辅助
本文研究史瓦西背景下洛伦兹破缺Kalb-Ramond场的平衡与线性扰动，发现零频模式塔及随黎曼耦合变负而出现的振荡不稳定性，其增强源于代数约束而非动力学失稳。
中文摘要 AI 辅助
我们研究了在固定史瓦西背景下，具有四次对称性破缺势和非最小黎曼耦合的洛伦兹破缺Kalb-Ramond场的平衡构型与线性扰动。对于静态球对称构型，电场分量由一个特征函数代数确定，该函数可发展出有限半径的二重根。接近这一退化构型时，单极电响应按$|\widehat e(\omega,r_c)|\propto(\gamma_c-\gamma)^{-1/2}$标度发散，而传播的单极振幅保持正则，表明增强源于代数约束而非动力学不稳定性。对于更高多极子，我们得到精确的零频模式塔，$\xi_{\ell n}=-(\ell+n+1)(\ell+n+2)/3$。对于$\ell=1$，有限频谱包含两个不同的低频分支。随着黎曼耦合变得更负，相应的纯虚不稳定模式合并并离开虚轴，成为$\omega_\pm=\pm\omega_R+i\omega_I$，产生振荡不稳定性。在合并点附近，实部劈裂遵循平方根律。
英文摘要
We study equilibrium configurations and linear perturbations of a Lorentz-violating Kalb--Ramond field with a quartic symmetry-breaking potential and a nonminimal Riemann coupling on a fixed Schwarzschild background. For static spherical configurations, the electric component is determined algebraically by a characteristic function that can develop a finite-radius double root. Approaching this degenerate configuration, the monopole electric response scales as $|\widehat e(ω,r_c)|\propto(γ_c-γ)^{-1/2}$, while the propagating monopole amplitude remains regular, showing that the enhancement originates from the algebraic constraint rather than from a dynamical instability. For higher multipoles, we obtain an exact tower of zero-frequency modes, $ξ_{\ell n}=-(\ell+n+1)(\ell+n+2)/3$. For $\ell=1$, the finite-frequency spectrum contains two distinct low-frequency branches. As the Riemann coupling becomes more negative, the corresponding purely imaginary unstable modes coalesce and leave the imaginary axis as $ω_\pm=\pmω_R+iω_I$, producing an oscillatory instability. Near the merger, the real-part splitting follows a square-root law.
发表机构
- Southeast University（东南大学）
- Shandong University（山东大学）
- North China Electric Power University（华北电力大学）
- Jining Normal University（济宁学院）
- Hunan Normal University（湖南师范大学）
机构由 AI 辅助整理，请以论文原文为准。
