标题： 孤子在引力平面波碰撞时空中的传播 显示英文标题

标题： Soliton propagation on a gravitational plane-wave collision spacetime

摘要： 我们提出了一类新的爱因斯坦方程的精确解，这些解通过Khan-Penrose过程构造，可以解释为在平面波碰撞时空背景中一对孤子的传播。 相互作用区域中的度规是通过将Rindler时空作为对角孤子扰动得到的，应用了Belinskii和Zakharov的逆散射方法（ISM），包含两个实极点和一对复共轭极点。 我们使用了一种非标准的归一化程序，得到了比标准ISM多两个参数的解。 我们分析了当度规的Killing部分的行列式趋于零时解的渐近行为，发现在这种情况下存在曲率奇点，除非解中包含的自由参数满足特定关系。 假设满足这一条件，我们证明了在上述极限情况下度规是正则的，并且在这种情况下，时空包含一个Killing柯西视界而不是曲率奇点。 这些解通过视界进行了解析延拓，在这种延拓中我们发现了一个与复极点的存在和传播相关的曲率奇点。 显示英文摘要

摘要： We present a new family of exact solutions of the Einstein equations, constructed through the Khan-Penrose procedure, that may be interpreted as representing the propagation of a pair of solitons, in the background of a plane-wave collision spacetime. The metric in the interaction region is obtained as a diagonal solitonic perturbation of Rindler's spacetime, applying the Belinskii and Zakharov Inverse Scattering Method (ISM), with two real poles and a pair of complex conjugate poles. We use a non-standard renormalization procedure, obtaining solutions that contain two more parameters than in the standard ISM. We analyze the asymptotic behaviour of the solutions in the limit where the determinant of the Killing part of the metric vanishes, finding in this limit a curvature singularity, except when the free parameters contained in the solutions satisfy a particular relation. Assuming this condition is satisfied, we show that the metric is regular in the above mentioned limit, and that the spacetimes contain in this case a Killing Cauchy horizon instead of a curvature singularity. The solutions are analytically extended through the horizon, and we find a curvature singularity in this extension, related to the presence and propagation of the complex poles.