Hadamard tail from initial data on the light cone
Hadamard tail from initial data on the light cone
复制标题
来自光锥初始数据的哈达玛尾部
DOI：
10.1103/physrevd.107.084008
复制
发表时间：
2022
影响因子：
5
通讯作者：
M. Casals
中科院分区：
文献类型：
--
作者：
David Q. Aruquipa;M. Casals
弯曲背景时空的场扰动通常不仅以光速传播，而且以所有更小的速度传播。这种所谓的“阿达玛尾”对波传播的贡献与各种情况有关，从经典的自力计算到量子粒子探测器之间的通信。计算尾波贡献的一种方法是利用光锥上的特征初始数据对齐次波动方程进行积分。然而，据我们所知，这种方法以前从未实现过，除非在平坦或共形平坦的时空中，从一点发出的零测地线不相交。在这项工作中，我们在黑洞玩具模型Pleba\ nski-Hacyan时空$\mathbb{M}_2\乘以\mathbb{S}^2$上实现了该方法。在这个时空中，我们通过计算标量场在其定义的任何地方（即任意点的最大正规邻域）的Hadamard尾来获得新的结果，并研究它如何随耦合常数的不同值而变化。这可以作为时空上的特征初始数据方法的概念证明，其中零测地线从点$do$交叉发出。
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 Pleba\'nski-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.