论文标题
Kerr黑洞的热敲响：夸张激发，费米 - 迪拉克统计和灰体因子
Thermal Ringdown of a Kerr Black Hole: Overtone Excitation, Fermi-Dirac Statistics and Greybody Factor
论文作者
论文摘要
我们发现，在巨大的黑洞和紧凑型物体的极端质量比率合并引起的早期响应中，克尔泛音之间存在明显的破坏性干扰，并且响声频谱显然遵循费米 - 迪拉克分布。我们从数值上计算出粒子浸入Kerr黑洞中引起的重力波的光谱幅度，并研究了多个准正常（QN）模式的激发。我们发现，环的开始时间是在信号的应变峰之前，对应于粒子通过光子球的时间。当黑洞具有近乎超级旋转时，KERR QN频率接近带有霍金温度的费米尼式哑光频率和超级频率的化学势。我们确实发现，光谱振幅的绝对平方显然遵循费米 - 迪拉克分布，具有基本模式的实际QN频率的化学势。将Boltzmann分布拟合到较高频率的数据中，发现最佳拟合温度接近鹰温度，尤其是对于快速旋转而言。在近超级极限中，重力波谱在超级频率$ω=μ_ {\ rm h} $处表现出可能的费米堕落性。我们表明，灰体因子，即黑洞的吸收横截面，导致费米 - 迪拉克分布。由于灰体因子是另一个无头发的黑洞，因此我们可以通过观察搜索$ω\gtrsimμ_ {\ rm h} $在不从ringdown提取QN模式的情况下观察到boltzmann分布来测试一般相对性。我们可以测量响起黑孔的质量和角动量，并可以通过测量灰色体谱上的灰体因子来探测KERR/CFT。
We find a significant destructive interference among Kerr overtones in the early ringdown induced by an extreme mass-ratio merger of a massive black hole and a compact object, and that the ringdown spectrum apparently follows the Fermi-Dirac distribution. We numerically compute the spectral amplitude of gravitational waves induced by a particle plunging into a Kerr black hole and study the excitation of multiple quasi-normal (QN) modes. We find that the start time of ringdown is before the strain peak of the signal and corresponds to the time when the particle passes the photon sphere. When the black hole has the near-extremal rotation, the Kerr QN frequencies are close to the fermionic Matsubara frequencies with the Hawking temperature and the chemical potential of the superradiant frequency. We indeed find that the absolute square of the spectral amplitude apparently follows the Fermi-Dirac distribution with the chemical potential of around the real QN frequency of the fundamental mode. Fitting the Boltzmann distribution to the data in higher frequencies, the best-fit temperature is found out to be close to the Hawking temperature, especially for rapid rotations. In the near-extremal limit, the gravitational-wave spectrum exhibits a would-be Fermi degeneracy with the Fermi surface at the superradiant frequency $ω= μ_{\rm H}$. We show that the greybody factor, i.e., the absorption cross section of a black hole, leads to the Fermi-Dirac distribution. As the greybody factor is another no-hair quantity of black holes, this opens a new possibility that we can test general relativity by observationally searching for the Boltzmann distribution in $ω\gtrsim μ_{\rm H}$ without extracting QN modes from ringdown. We could measure the mass and angular momentum of ringing black holes and could probe the Kerr/CFT by measuring the greybody factor imprinted on the ringdown spectrum.
