论文标题
重力脉冲波散射和Geroch组
Gravitational Pulse Wave Scattering and the Geroch group
论文作者
论文摘要
圆柱重力脉冲波是圆柱引力波，其脉冲轮廓朝着径向的方向上。圆柱引力脉冲波的动力学由一个二维集成的Sigma模型控制，该模型具有无限的尺寸隐藏对称性，称为Geroch群。 Piran，Safier和Katz通过对KERR度量的双重分析延续获得了单个脉冲波的精确溶液。他们的解决方案描述了从无穷大到达的脉冲波，从对称轴上弹跳并返回无穷大。在本说明中，我们通过双重分析延续对双脉冲度量获得了双脉冲波的精确解决方案。新解决方案描述了一对从无穷大到达，彼此散射并返回无穷大的脉冲波。脉冲相互穿过，并像普通的孤子散射一样完整地出现形状。与普通的孤子散射不同，没有时间延迟。该度量没有出现在双Kerr公制中的圆锥形奇异性。将来，了解Geroch组如何在引力脉冲波散射的量子版本中表现出来会很有趣。
Cylindrical gravitational pulse waves are cylindrical gravitational waves with a pulse profile in the radial direction. The dynamics of cylindrical gravitational pulse waves is governed by a two dimensional integrable sigma model with an infinite dimensional hidden symmetry called the Geroch group. Piran, Safier, and Katz obtained an exact solution for a single pulse wave by making a double analytic continuation of the Kerr metric. Their solution describes a pulse wave that arrives from infinity, bounces off the symmetry axis, and returns to infinity. In this note, we obtain an exact solution for a double pulse wave by making a double analytic continuation of the double Kerr metric. The new solution describes a pair of pulse waves that arrive from infinity, scatter through each other, and return to infinity. The pulses pass through each other and emerge with their shapes intact, as in ordinary soliton scattering. Unlike ordinary soliton scattering, there is no time delay. The metric is free of the conical singularity that appears in the double Kerr metric. In the future, it would be interesting to understand how the Geroch group manifests in the quantum version of gravitational pulse wave scattering.
