论文标题
Kerr黑洞的潮汐爱数字
Tidal Love Numbers of Kerr Black Holes
论文作者
论文摘要
Kerr黑洞是否会潮汐变形的开放问题对基本物理和重力波天文学具有深远的影响。我们考虑一个嵌入在弱且缓慢变化但否则任意的多极潮汐环境中的Kerr黑洞。通过求解量规不变的Weyl scalar $ψ_0$的静态Teukolsky方程，并通过将相应的度量扰动重建在ingo辐射仪中，用于一般的谐波指数$ \ ell $，我们计算Kerr黑洞对Tidal Field的线性响应。对于Schwarzschild黑洞和旋转黑洞的轴对称扰动，这种线性响应的消失相同。但是，对于旋转黑洞的非轴对称扰动，线性响应不会消失，并且有助于扰动Kerr几何形状的Geroch-Hansen多极矩。作为一种应用，我们明确计算旋转黑洞的潮汐爱情数字，这些爱情数字将诱导的四极矩矩与四极极潮汐场融为一体，以在黑洞旋转中进行线性顺序，并介绍了潮汐爱量tensor的相应概念。最后，我们表明那些引起的四极矩与潮汐体与潮汐重力环境相互作用的潮汐扭矩的众所周知的物理现象密切相关。
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $ψ_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $\ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanishes identically for a Schwarzschild black hole and for an axisymmetric perturbation of a spinning black hole. For a nonaxisymmetric perturbation of a spinning black hole, however, the linear response does not vanish, and it contributes to the Geroch-Hansen multipole moments of the perturbed Kerr geometry. As an application, we compute explicitly the rotational black hole tidal Love numbers that couple the induced quadrupole moments to the quadrupolar tidal fields, to linear order in the black hole spin, and we introduce the corresponding notion of tidal Love tensor. Finally, we show that those induced quadrupole moments are closely related to the well-known physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.
