论文标题
hadamard尾巴从光锥上的初始数据
Hadamard Tail from Initial Data on the Light Cone
论文作者
论文摘要
弯曲的背景时空的场扰动通常不仅在光速下传播，而且在所有较小的速度下也会传播。这种所谓的$ hadamard \，尾巴$对波传播的贡献在各种环境中都相关，从经典的自力计算到量子粒子探测器之间的通信。一种计算此尾部贡献的方法是使用光锥上的特征初始数据整合均匀波方程。但是，据我们所知，除了在平坦或同型式空间时，这种方法从未实施过，在某个点上发出的无效测量值并没有交叉。在这项工作中，我们在黑洞玩具模型Plebański-Hacyan SpaceTime上实现了此方法，$ \ Mathbb {M} _2 \ times \ times \ Mathbb {s}^2 $。我们通过计算定义的标量场的Hadamard尾巴（即，在任意点的最大正常邻域中），并研究它如何在耦合常数值的各种值方面变化，从而获得了新的结果。这是对空间特征初始数据方法的概念验证，而无效的大地测量学从点$ do $ cross发出。
Field perturbations of a curved background spacetime generally propagate not only at the speed of light but also at all smaller velocities. This so-called $Hadamard\,tail$ contribution to wave propagation is relevant in various settings, from classical self-force calculations to communication between quantum particle detectors. One method for calculating this tail contribution is by integrating the homogeneous wave equation using Characteristic Initial Data on the light cone. However, to the best of our knowledge, this method has never been implemented before except in flat or conformally-flat spacetimes, where null geodesics emanating from a point do not cross. In this work, we implement this method on the black hole toy model Plebański-Hacyan spacetime, $\mathbb{M}_2\times\mathbb{S}^2$. We obtain new results in this spacetime by calculating the Hadamard tail of a scalar field everywhere where it is defined (namely, in the maximal normal neighbourhood of an arbitrary point) and investigate how it varies for various values of the coupling constant. This serves as a proof-of-concept for the Characteristic Initial Data method on spacetimes where null geodesics emanating from a point $do$ cross.
