AI 中文总结
该研究计算克尔时空线性场微扰的特克尔方程推迟格林函数的高阶晚期拖尾，通过小频率展开获取渐近表达式，得到一般自旋\(s\)的拖尾幂次及引力微扰拖尾系数，还提供相关量展开及笔记本，方便特定\(s\)值展开查询。
AI 中文摘要
我们计算了（次极端）克尔时空线性场微扰的特克尔方程推迟格林函数的高阶晚期拖尾。我们在固定的球谐函数\(\ell\)和方位数\(m\)下，对场点计算到前三阶拖尾：在有限半径（远离事件视界）处，对于大的博伊尔 - 林德奎斯特时间\(t\)；沿着未来事件视界\(\mathscr{H}^+\)，对于大的内向爱丁顿 - 芬克尔斯坦坐标\(v\)；以及沿着未来类光无穷远\(\mathscr{I}^+\)，对于大的外向爱丁顿 - 芬克尔斯坦坐标\(u\)。我们得到了一般整数场自旋\(s\)的拖尾幂次，以及引力（\(s = -2\)）微扰的拖尾系数。我们的渐近表达式包括已知的主导幂律（一般）拖尾，以及它们的高阶对数修正。由于我们得到了一般\(\ell\)和\(m\)模式的高阶展开，所以可以很容易地推断出\(s = -2\)时完整推迟格林函数的显式展开（以及一般整数\(s\)的衰减幂次）。我们从推迟格林函数在频域的傅里叶模式的小频率展开中得到晚期渐近表达式。相应地，我们还提供了散射理论中各种感兴趣量的小频率展开。我们还附上了两个笔记本，它们提供了特定\(s\)值的展开：一个笔记本提供了一般\(\ell\)的前三个主导阶的展开，另一个提供了特定\(\ell\)值的任意阶展开。
英文摘要
We calculate high-order late-time tails of the retarded Green function of the Teukolsky equation for linear field perturbations of (subextremal) Kerr spacetime. We calculate these tails at a fixed spheroidal harmonic $\ell$ and azimuthal number $m$ up to the first three orders for the field point: at finite radius (away from the event horizon) for large Boyer-Lindquist time $t$; along the future event horizon $\mathscr{H}^+$ for large ingoing Eddington-Finkelstein coordinate $v$; and along future null infinity $\mathscr{I}^+$ for large outgoing Eddington-Finkelstein coordinate $u$. We obtain the tail powers for generic integer field spin $s$ and the tail coefficients specifically for gravitational ($s=-2$) perturbations. Our asymptotics include the known leading power-law (generic) tails, respectively,$t^{-2\ell-3}$, $e^{imΩ_H v}v^{-2\ell-3-b}$ (where $b=1$ for $s>0, m=0$ and $b=0$ otherwise, and where $Ω_H$ is the angular velocity of the event horizon) and $u^{-\ell+s-2}$, as well as their higher-order logarithmic corrections: $t^{-2\ell-5}\ln t$, $e^{imΩ_H v}v^{-2\ell-5-b}\ln v$ and $u^{-\ell+s-3}\ln u$ (as well as $u^{-\ell+s-4}\ln^2 u$). Since we obtain the high-order expansions for modes for generic $\ell$ and $m$, we can readily infer the explicit expansions of the {\it full} retarded Green function for $s=-2$ (and its decay powers for generic integer $s$). We obtain the late-time asymptotics from small-frequency expansions of the Fourier modes of the retarded Green function in the frequency domain. Accordingly, we also provide small-frequency expansions of various quantities of interest in the scattering theory. We also attach two notebooks which provide expansions for specific values of $s$: one notebook provides them to the first three leading orders for generic $\ell$ and the other one to arbitrary order for specific values of $\ell$.
Comments28 pages, 11 figures, 2 ancillary notebooks
