Rotating black holes experience dynamical tides

We calculate the tidal response of a rotating black hole from the Teukolsky equation in the near-horizon and small-frequency regime. While the static tidal Love number of an arbitrarily rotating black hole is still zero, the dynamical tidal Love number is not; rather, it is proportional to the angular velocity of the black hole -- in the linear order of frequency -- and to the square of the angular velocity of the black hole -- in the zeroth order. Intriguingly, the zero-frequency limit of the dynamical tidal response function is not equal to the static tidal response function. We demonstrate that these results hold true for an extremal rotating black hole as well, with the dynamical tidal Love numbers being non-zero. This shows that Kerr black holes experience dynamical tides.

我们从近视界和小频率区域的特克尔斯基方程计算旋转黑洞的潮汐响应。虽然任意旋转黑洞的静态潮汐洛夫数仍然为零，但动态潮汐洛夫数不为零；相反，它与黑洞的角速度成正比——在频率的线性阶上——并且与黑洞角速度的平方成正比——在零阶上。有趣的是，动态潮汐响应函数的零频率极限不等于静态潮汐响应函数。我们证明这些结果对于极端旋转黑洞也成立，其动态潮汐洛夫数不为零。这表明克尔黑洞会经历动态潮汐。