论文标题
与共形的爱因斯坦场方程的特征初始价值问题的存在改善
Improved existence for the characteristic initial value problem with the conformal Einstein field equations
论文作者
论文摘要
我们将卢克（Luk）对特征初始价值问题的分析通常相对论分析，以对共形的爱因斯坦磁场方程的渐近特征问题，以证明在给出数据的集合的邻里中，证明了解决方案的局部存在。特别是，我们沿着null无穷大的狭窄矩形获得了溶液的存在，这反过来对应于物理时空的渐近区域中的无限结构域。这一结果概括了Kánanár通过Rendall的减少策略来解决特征初始价值问题的局部解决方案的工作。在分析共形的爱因斯坦方程时，我们利用了纽曼 - 芬罗斯形式主义和因J. Stewart引起的量规。
We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood of the set on which the data are given. In particular, we obtain existence of solutions along a narrow rectangle along null infinity which, in turn, corresponds to an infinite domain in the asymptotic region of the physical spacetime. This result generalises work by Kánnár on the local existence of solutions to the characteristic initial value problem by means of Rendall's reduction strategy. In analysing the conformal Einstein equations we make use of the Newman-Penrose formalism and a gauge due to J. Stewart.
