用宇宙学数据函数求解观测坐标系下的爱因斯坦场方程：具有宇宙学常数的球对称宇宙
Solving Einstein Field Equations in Observational Coordinates with Cosmological Data Functions: Spherically Symmetric Universes with Cosmological Constant
摘要：
扩展了Araújo和Stoeger [1]提出并在Araújo { \it et al} [2]中改进的方法，我们已经展示了如何从我们过去光锥上的FLRW宇宙学数据构建充满灰尘的$Λ\neq 0$ Friedmann-Lema\^itre-Robertson-Walker（FLRW）宇宙学模型。除了在其本身的权利感兴趣-演示如何这样的数据完全确定的模型-它也说明了在平面的情况下如何更一般的球对称（SS）爱因斯坦场方程可以集成在观测坐标与数据适合FLRW形式排列在我们过去的光锥，从而显示了这些数据如何确定FLRW宇宙--这不是{ \it先验}明显的。它还示出了如何整合这些精确的SS方程，在数据不是FLRW的情况下，时空是不知道是平坦的。无论是平坦的还是非平坦的情况，都必须有观测者区域（角直径）距离的最大值的数据，以及发生这种情况时的红移$z_{max}$。这使得能够确定真空能量密度$μ_Λ$，否则其将保持未确定。
英文摘要：
Extending the approach developed by Araújo and Stoeger [1] and improved in Araújo {\it et al} [2], we have shown how to construct dust-filled $Λ\neq 0$ Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) cosmological models from FLRW cosmological data on our past light cone. Apart from being of interest in its own right -- demonstrating how such data fully determines the models -- it is also illustrated in the flat case how the more general spherically symmetric (SS) Einstein field equations can be integrated in observational coordinates with data fit to FLRW forms arrayed on our past light cone, thus showing how such data determines a FLRW universe -- which is not {\it a priori} obvious. It is also shown how to integrate these exact SS equations, in cases where the data are not FLRW, and the space-time is not known to be flat. It is essential for both flat and non-flat cases to have data giving the maximum of the observer area (angular-diameter) distance, and the redshift $z_{max}$ at which that occurs. This enables the determination of the vacuum-energy density $μ_Λ$, which would otherwise remain undetermined.
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