引力波连续谱中的束缚态
Bound states in the continuum of gravitational waves
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中文总结 AI 辅助
本文证明引力波连续谱中存在束缚态，通过面内周期性扰动构造指数局域的真空解，其与平面波偏振对应且由对称性保护，实现引力波局域化。
中文摘要 AI 辅助
连续谱中的束缚态（BICs）是普遍存在的波动现象，但尚未在引力波（GWs）中得到证实。本文表明，在平面 $z = 0$ 上指数局域的面内周期性扰动，会导致该平面上的分布性表面能量张量，并且是线性化爱因斯坦场方程在平面外的正则真空解（$T_{\mu \nu} = 0$）。这些解是通过从度规扰动张量显式计算里奇张量分量和里奇标量而获得的。为了满足每个真空解（$R_{{\sigma \nu}_{(+, \times)}} = 0$ 和 $R_{{}_{(+, \times)}} = 0$），需要不同的表面极化激元型色散关系。这些束缚扰动指数衰减为平坦度规（$h_{{BIC}_{(+,\times)}} \propto e^{- k_z |z|}$），并且每个局域度规对应于不同的平面引力波偏振（$+,\times$）。满足洛伦兹规范条件的解存在于动量空间的 $\Gamma$ 点，位于传播引力波波矢的连续谱内。周期性扰动的晶胞中的应变，在 $C_2$ 面内旋转下，相对于相应的平面引力波具有相反的宇称，这使得它们在对称性上与传播对应物不相容，表明通过对称性保护实现局域化。
英文摘要
Bound states in the continuum (BICs) are ubiquitous wave phenomena, but have not yet been demonstrated for gravitational waves (GWs). Here, in-plane periodic perturbations, exponentially localized at the plane $z = 0$, are shown to lead to distributional surface energy tensors at this plane and to be regular vacuum solutions ($T_{μν} = 0$) of the linearized Einstein field equations outside of it. These are achieved by explicitly calculating the Ricci tensor components and the Ricci scalar from the metric perturbation tensor. To fulfill each vacuum solution ($R_{{σν}_{(+, \times)}} = 0$ and $R_{{}_{(+, \times)}} = 0$), different surface polariton-like dispersions are required. These bound perturbations decay exponentially to a flat metric ($h_{{BIC}_{(+,\times)}} \propto e^{- k_z |z|}$), and each localized metric has a correspondence to a different planar GW polarization ($+,\times$). The Lorenz gauge-fulfilling solutions exist at the $Γ$ point in momentum space, dwelling within the continuum of wavevectors of propagating GWs. The strains in the unit cell of the periodic perturbations have opposite parities relative to the corresponding planar GWs under a $C_2$ in-plane rotation, making them incompatible by symmetry with their propagating counterpart, indicating localization via symmetry protection.
发表机构
- Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）
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