论文标题
黑洞的韦尔定律
A Weyl's law for black holes
论文作者
论文摘要
我们讨论了黑洞的准正常模式的Weyl定律，该法律恢复了紧凑型区域中拉普拉斯式特征值的标准Weyl定律的结构特征。具体而言，计数函数的渐近学$ n（ω）$的$（d+1）$ - dimensional黑洞遵循power-law $ n（ω）\ sim \ sim \ sim \ sim \ sim \ sim \ sim \ sim \ sim \ simrm {vol} _d _d _d^{ $ \ mathrm {vol} _d^{\ mathrm {eff}} $由黑洞几何形状的轻捕获和衰减属性确定的有效音量。为Schwarzschild黑洞提供了封闭形式，并提出了用于通用黑洞的准正常模式Weyl定律。作为一种应用，这种Weyl定律可以对时空的有效维度和实际天体黑洞的相关谐振尺度进行探测，这是在观察到的二进制黑洞合并的响声信号中足够多的泛音。
We discuss a Weyl's law for the quasi-normal modes of black holes that recovers the structural features of the standard Weyl's law for the eigenvalues of the Laplacian in compact regions. Specifically, the asymptotics of the counting function $N(ω)$ of quasi-normal modes of $(d+1)$-dimensional black holes follows a power-law $N(ω)\sim \mathrm{Vol}_d^{\mathrm{eff}}ω^d$, with $\mathrm{Vol}_d^{\mathrm{eff}}$ an effective volume determined by the light-trapping and decay properties of the black hole geometry. Closed forms are presented for the Schwarzschild black hole and a quasi-normal mode Weyl's law is proposed for generic black holes. As an application, such Weyl's law could provide a probe into the effective dimensionality of spacetime and the relevant resonant scales of actual astrophysical black holes, upon the counting of sufficiently many overtones in the observed ringdown signal of binary black hole mergers.
