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arXiv 0806.1597gr-qc
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平面对称时空中的Shock Waves

Shock Waves in Plane Symmetric Spacetimes

Alan D. Rendall, Fredrik Ståhl

摘要:

我们认为爱因斯坦方程耦合到欧拉方程在平面对称,紧凑的空间切片和常数平均曲率时间。我们表明,对于各种各样的状态方程和一个大类的初始数据,经典的解决方案在有限时间内崩溃。关键的数学结果是一个新的定理的崩溃的解决方案系统的平衡法。我们还表明,如果能量密度和速度的空间导数是有界的,表示的击穿是真正由于形成冲击波的解决方案的延伸是可能的。

英文摘要:

We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data, classical solutions break down in finite time. The key mathematical result is a new theorem on the breakdown of solutions of systems of balance laws. We also show that an extension of the solution is possible if the spatial derivatives of the energy density and the velocity are bounded, indicating that the breakdown is really due to the formation of shock waves.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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