论文标题
Einstein-Scalar野外系统的半球体非振荡大爆炸奇异的空间
Semiglobal non-oscillatory big bang singular spacetimes for the Einstein-scalar field system
论文作者
论文摘要
我们为爱因斯坦方程构建半光彩的奇异空间，耦合到无质量标量场。与Belinskii，Khalatnikov，Lifshitz或BKL的启发式分析一致，因此由于标量场而没有振荡。 （这要比爱因斯坦真空方程的振荡BKL启发式方法简单得多。）先前的结果是由于Andersson和Rendall在实际分析案例中以及Rodnianski和Speck在平滑的近空间 - flat-Flrw案例中。与Andersson和Rendall类似，我们在奇异性上提供了渐近数据，我们将其称为最终数据，但我们的构造不仅限于实际分析解决方案。本文是针对更微妙的真空案例的工具的测试应用（爱因斯坦方程的分级代数配方和过滤）。我们使用同源代数工具来构建形式的系列解决方案，然后使用对称双曲能量估计来构建一个由正式截断构成的真实解决方案。我们猜想地图从最终数据到初始数据的图像是一组各向异性初始数据。
We construct semiglobal singular spacetimes for the Einstein equations coupled to a massless scalar field. Consistent with the heuristic analysis of Belinskii, Khalatnikov, Lifshitz or BKL for this system, there are no oscillations due to the scalar field. (This is much simpler than the oscillatory BKL heuristics for the Einstein vacuum equations.) Prior results are due to Andersson and Rendall in the real analytic case, and Rodnianski and Speck in the smooth near-spatially-flat-FLRW case. Similar to Andersson and Rendall we give asymptotic data at the singularity, which we refer to as final data, but our construction is not limited to real analytic solutions. This paper is a test application of tools (a graded Lie algebra formulation of the Einstein equations and a filtration) intended for the more subtle vacuum case. We use homological algebra tools to construct a formal series solution, then symmetric hyperbolic energy estimates to construct a true solution well-approximated by truncations of the formal one. We conjecture that the image of the map from final data to initial data is an open set of anisotropic initial data.
