arXiv 2201.076622022-01-19gr-qchep-th

引力脉冲波散射与Geroch群

Gravitational Pulse Wave Scattering and the Geroch group

Robert F. Penna

摘要：

圆柱形引力脉冲波是在径向方向上具有脉冲轮廓的圆柱形引力波。圆柱形引力脉冲波的动力学是由一个二维可积西格玛模型控制的，该模型具有无限维的隐对称性，称为Geroch群。皮兰、萨菲尔和卡茨通过对克尔度规进行双重解析延拓，得到了单个脉冲波的精确解。他们的解描述了一个脉冲波从无穷远到达，从对称轴反弹，然后返回无穷远。本文通过对双Kerr度规进行双解析延拓，得到了双脉冲波的精确解。新的解描述了一对脉冲波，它们从无穷远到达，相互散射，然后返回无穷远。脉冲相互穿过，并以它们的形状完整地出现，就像在普通的孤子散射中一样。与普通的孤子散射不同，它没有时间延迟。该度规没有出现在双克尔度规中的圆锥奇点。在未来，了解Geroch群如何在引力脉冲波散射的量子版本中表现出来将是有趣的。

英文摘要：

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.

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