论文标题
斯托克斯现象和鹰辐射
Stokes phenomenon and Hawking Radiation
论文作者
论文摘要
我们通过得出单向连接公式来计算Kerr黑洞的半经典衰减速率，将近地平线溶液与无穷大的传出溶液相关联。特别是，我们讨论了Stokes现象的相关性，并通过使用Stokes图来展示它如何导致类似玻尔兹曼的热量因子。我们还给出了半经典的灰色因子$ e^{ - 2s}的确切结果，其中$ s $是领先的订单WKB操作。我们将结果与Maldacena和Strominger的作品进行对比[Phys。 Rev. D 56，4975（1997）]，其中通过渐近匹配在本地计算了旋转黑洞的发射光谱。我们发现，如预期的那样，对于渐近匹配公式的半经典衰减速率的相对误差在大角动量（$ l $）的极限下降低。在此限制中，该操作假定一个紧凑的形式：$ 2S \ sim（2 l+1）（\ text {log} \ left（\ frac {16} {z_0} \ right）-1）$，其中$ z_0 $是散射电位的关键点（零）形成的交叉比率。
We compute the semiclassical decay rate for Kerr black hole by deriving a one-way connection formula, relating the near horizon solution to the outgoing solution at infinity. In particular, we discuss the relevance of the Stokes phenomenon and show how it leads to a Boltzmann-like thermal weight factor by making use of the Stokes diagrams. We also give the exact result for the semiclassical greybody factor $e^{-2S}, $ where $S$ is the leading order WKB action. We contrast our results with Maldacena and Strominger's work [Phys. Rev. D 56, 4975 (1997)], where the emission spectrum for a rotating black hole was computed locally via asymptotic matching. We find that the relative error of semiclassical decay rate with respect to asymptotic matching formula diminishes in the limit of large angular momentum, $l$, as expected. In this limit, the action assumes a compact form: $2S \sim (2 l+1) (\text{Log} \left( \frac{16 }{z_0}\right)-1)$, where $z_0$ is the cross ratio formed by the critical points (zeroes) of the scattering potential.
