标题： 来自D维冲击波碰撞的辐射：二维约化和卡特尔-彭罗斯图 显示英文标题

标题： Radiation from a D-dimensional collision of shock waves: Two dimensional reduction and Carter-Penrose diagram

摘要： 我们分析了二维（2D）降维背景的因果结构，该背景用于处理两个一维（$D$- 维度）Aichelburg-Sexl引力冲击波的迎面碰撞的微扰处理。 在定义所有因果边界之后，即碰撞的未来光锥和未来观察者的过去光锥，我们使用两种独立的方法获得特征坐标。 第一种方法是通过参数表示法构造定义各种光锥的零光线的几何构造。 第二种方法是将问题的二维降维波动算子变换为双曲形式。 然后将特征坐标紧凑化，使我们能够在共形Carter-Penrose图中表示所有的因果光线。 我们的构造在微扰理论的所有阶次上都成立。 特别是，在每一阶上，我们可以轻松识别出现在微扰展开中的源函数和Green函数的奇异性，这对于成功地用这种方法评估任何更高阶修正至关重要。 显示英文摘要

摘要： We analyse the causal structure of the two dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two $D$-dimensional Aichelburg-Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter-Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green's functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.