论文标题
分布指标和爱因斯坦 - 希尔伯特重力的动作原理
Distributional Metrics and the Action Principle of Einstein-Hilbert Gravity
论文作者
论文摘要
在这项工作中，指定了广义的kerr-schild类别的子类，并指定了ricci张量（无论指数的位置如何）在几何学的所谓谱函数中是线性的。考虑到哥伦布的广义函数的非线性理论，该结果被扩展到适用于一类相关的分布kerr-schild几何形状，然后用于为这些奇异空间制定变异原理。更具体地说，在这方面表明，即使相应的广义Kerr-Schild代表之一的指标包含一个通用的Delta函数，也可以执行适当正常的爱因斯坦 - 希尔伯特动作的变化，即使在适当的限制Delta分布中收敛。
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry. Considering Colombeau's nonlinear theory of generalized functions, this result is extended to apply to an associated class of distributional Kerr-Schild geometries, and then used to formulate a variational principle for these singular spacetimes. More specifically, it is shown in this regard that a variation of a suitably regularized Einstein-Hilbert action can be performed even if the metric of one of the corresponding generalized Kerr-Schild representatives contains a generalized delta function that converges in a suitable limit to a delta distribution.
