碰撞平面引力波的连续Riemann-Hilbert问题
A continuous Riemann-Hilbert problem for colliding plane gravitational waves
摘要：
本文提出了一种求解碰撞平面引力波特征初值问题的新方法。它与Alekseev和Griffiths在2001年的方法有着广泛的相似之处，但是我们使用了一种具有Riemann-Hilbert问题（RHP）的逆散射方法，该方法允许转换为具有非奇异函数积分方程解的连续RHP。在这个过程中的歧义导致建设一个家庭的时空包含解决方案的IVP。因此，所描述的技术也用作有趣的解决方案生成方法。该程序的例子是扩展Szekeres类碰撞波时空与2个额外的实参数。得到的解决方案似乎具有一种新型的脉冲波，这是圆极化的极限情况。
英文摘要：
We present the foundations of a new solution technique for the characteristic initial value problem (IVP) of colliding plane gravitational waves. It has extensive similarities to the approach of Alekseev and Griffiths in 2001, but we use an inverse scattering method with a Riemann-Hilbert problem (RHP), which allows for a transformation to a continuous RHP with a solution given in terms of integral equations for non-singular functions. Ambiguities in this procedure lead to the construction of a family of spacetimes containing the solution to the IVP. Therefore the described technique also serves as an interesting solution generating method. The procedure is exemplified by extending the Szekeres class of colliding wave spacetimes with 2 additional real parameters. The obtained solution seems to feature a limiting case of a new type of impulsive waves, which are circularly polarised.
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