Points of general relativistic shock wave interaction are ‘regularity singularities’ where space–time is not locally flat
Points of general relativistic shock wave interaction are ‘regularity singularities’ where space–time is not locally flat
复制标题
广义相对论激波相互作用的点是时空局部不平坦的“规则奇点”
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
B. Temple
中科院分区：
文献类型：
--
作者：
Moritz Reintjes;B. Temple
我们表明，在广义相对论中，在激波相互作用点附近的C1，1坐标变换类中，球对称时空中引力度规张量的正则性不能从C 0，1提升到C1，1，而不迫使度规张量的行列式在相互作用点处为零。这与Israel 9的定理相反，Israel 9的定理指出这样的坐标变换总是存在于光滑的单激波表面上一点的邻域内。因此，这些结果意味着，激波相互作用点代表了时空中演化的完美流体的一种新的正则性奇点，这种奇点在物理上非常有意义，可以从光滑初始数据的演化中形成，但在任何坐标变换下，时空都不是局部闵可夫斯基的。特别地，在正则性奇点处，度量的二阶导数中的δ函数源存在于C 1，1-atlas的所有坐标系中，但由于取消，完全黎曼曲率张量保持超范数有界。
We show that the regularity of the gravitational metric tensor in spherically symmetric space–times cannot be lifted from C 0,1 to C 1,1 within the class of C 1,1 coordinate transformations in a neighbourhood of a point of shock wave interaction in General Relativity, without forcing the determinant of the metric tensor to vanish at the point of interaction. This is in contrast to Israel9s theorem, which states that such coordinate transformations always exist in a neighbourhood of a point on a smooth single shock surface. The results thus imply that points of shock wave interaction represent a new kind of regularity singularity for perfect fluids evolving in space–time, singularities that make perfectly good sense physically, that can form from the evolution of smooth initial data, but at which the space–time is not locally Minkowskian under any coordinate transformation. In particular, at regularity singularities, delta function sources in the second derivatives of the metric exist in all coordinate systems of the C 1,1 -atlas, but due to cancellation, the full Riemann curvature tensor remains supnorm bounded .