以光速传播的广义相对论冲击波
General Relativistic Shock-Waves Propagating at the Speed of Light
摘要：
我们研究了当传播速度等于光速时爱因斯坦方程的激波解。这项工作扩展了Smoller和Temple的激波匹配理论，该理论描述了当时空度规在超曲面上仅为Lipschitz连续时爱因斯坦方程的解，并将其扩展到类光情况。在简单介绍了广义相对论之后，我们在介绍了Barrabes和Israel对第二基本型的一个已知推广之后，发展了激波匹配理论的扩展。在理论的发展，我们证明了广义第二基本型的匹配单独是不是一个充分条件保持跨接口的守恒条件。然后，我们使用这个理论来构建一个新的精确解的爱因斯坦方程，可以解释为一个传出的球形冲击波，以光速传播。该解是通过匹配弗里德曼罗伯逊沃克（FRW）度规，这是一个几何模型的宇宙，托尔曼奥本海默勒夫（TOV）度规，它模拟了一个静态的等温时空。在震动的每一侧，声速是恒定的，并且是亚发光的。此外，激波前缘的压力和密度较小，这与经典气体动力学中的Lax熵条件相一致。然而，冲击速度大于所有特征速度。该解决方案还产生了一个令人惊讶的结果，即解决方案不等于先前已知的亚发光解决方案的极限，因为它们倾向于光速。
英文摘要：
We investigate shock-wave solutions of the Einstein equations in the case when the speed of propagation is equal to the speed of light. The work extends the shock matching theory of Smoller and Temple, which characterizes solutions of the Einstein equations when the spacetime metric is only Lipschitz continuous across a hypersurface, to the lightlike case. After a brief introduction to general relativity, we develop the extension of a shock matching theory after introducing a previously known generalization of the second fundamental form by Barrabes and Israel. In the development of the theory we demonstrate that the matching of the generalized second fundamental form alone is not a sufficient condition for conservation conditions to hold across the interface. We then use this theory to construct a new exact solution of the Einstein equations that can be interpreted as an outgoing spherical shock wave that propagates at the speed of light. The solution is constructed by matching a Friedman Robertson Walker (FRW) metric, which is a geometric model for the universe, to a Tolman Oppenheimer Volkoff (TOV) metric, which models a static isothermal spacetime. The sound speeds, on each side of the shock, are constant and sub-luminous. Furthermore, the pressure and density are smaller at the leading edge of the shock, which is consistent with the Lax entropy condition in classical gas dynamics. However, the shock speed is greater than all the characteristic speeds. The solution also yields a surprising result in that the solution is not equal to the limit of previously known subluminous solutions as they tend to the speed of light.
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。
