发表机构
University of South Carolina（南卡罗来纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在动力学Chern-Simons引力中解析求解非旋转黑洞的低频散射，给出引力子-赝标量转换概率和灰体吸收不对称性的精确公式，揭示宇称破缺效应及其与准正则模分裂的联系。
AI 中文摘要
我们研究了在动力学Chern-Simons（dCS）引力中，引力波和赝标量波在非旋转黑洞上的低频散射，其中轴向（奇宇称）引力扇区与动力学赝标量不可约地耦合，而极向扇区保持广义相对论形式。在一阶无量纲耦合参数zeta = (ell_CS/M)^4下，利用匹配渐近展开，我们获得了引力子到赝标量转换概率的精确闭式解，d_2 = 3(pi^2-9)^2/8，以及在经过证明的超越基中对四极（ell=2）通道的引力子灰体（吸收）不对称性kappa_2 = (21/80) pi^4 + (27/8) pi^2 - 89833/1536的高精度重构。两者均化简为pi^4、pi^2和有理数的组合，在重构基中不含ln2或奇次zeta项；相比之下，透射相位扇区包含一个解析推导的zeta(3)-9/8静态积分，而其整体匹配前置因子通过数值确定。主导反射相位不对称性为零，因此在主导低频阶上，反射波不会印上偏振旋转，而透射相位中仍存在次主导的O(omegazeta)不对称性。归一化通量不对称性在几何光学极限下与1/(Momega)^2衰减数值一致，其中主导的剩余通量效应是转换损失。匹配渐近结果通过与直接双通道积分对比检验，而决定kappa_2的一维积分在解析控制的超越基内以高精度评估。这些结果为将dCS在吸收和模式转换中的宇称破缺与轴向/极向准正则模分裂联系起来提供了解析目标。
英文摘要
We study the low-frequency scattering of gravitational and pseudoscalar waves off a non-rotating black hole in dynamical Chern-Simons (dCS) gravity, where the axial (odd-parity) gravitational sector is irreducibly coupled to the dynamical pseudoscalar while the polar sector remains general relativistic. Working to first order in the dimensionless coupling zeta = (ell_CS/M)^4 and using matched asymptotic expansions, we obtain an exact closed form for the graviton-to-pseudoscalar conversion probability, d_2 = 3(pi^2-9)^2/8, and a high-precision reconstruction, in a proven transcendental basis, of the graviton greybody (absorption) asymmetry, kappa_2 = (21/80) pi^4 + (27/8) pi^2 - 89833/1536, for the quadrupole (ell=2) channel. Both reduce to combinations of pi^4, pi^2, and rational numbers, with no ln2 or odd-zeta terms in the reconstructed basis; the transmission-phase sector, by contrast, contains an analytically derived zeta(3)-9/8 static integral, while its overall matching prefactor is identified numerically. The leading reflection-phase asymmetry vanishes, so that no polarization rotation is imprinted on the reflected wave at leading low-frequency order, while a subleading O(omegazeta) asymmetry remains in the transmitted phase. The normalized flux asymmetries are numerically consistent with a 1/(Momega)^2 falloff in the geometric-optics limit, where the leading remaining flux effect is conversion loss. The matched-asymptotic results are checked against direct two-channel integration, while the one-dimensional integral determining kappa_2 is evaluated to high precision within an analytically controlled transcendental basis. The results provide analytic targets linking dCS parity violation in absorption and mode conversion to the axial/polar quasinormal-mode splitting.
Comments18 pages, 2 figures, 6 tables. Submitted to General Relativity and Gravitation. Reproducibility package: Zenodo doi:10.5281/zenodo.23078252
