标题： 关于“双曲面”真空爱因斯坦方程的柯西数据和“-null infinity-”光滑性障碍 显示英文标题

标题： On ``hyperboloidal'' Cauchy data for vacuum Einstein equations and obstructions to smoothness of ``null infinity''

摘要： 多项工作表明，在光无穷远处引力场的 Bondi--Sachs--Penrose 衰减条件并不能一般地代表渐近平直时空。我们对“渐近双曲面”初值的约束方程进行了详细分析，发现对数项通常会在渐近展开中出现。这些项在对应的 Bondi--Sachs--Penrose 展开中不存在，并且可以与明确的几何量相关联。然而，我们已经证明存在一类“非典型”的约束方程解的大类，它们的演化会生成满足 Bondi--Sachs--Penrose 光滑性条件的空间-时间。 显示英文摘要

摘要： Various works have suggested that the Bondi--Sachs--Penrose decay conditions on the gravitational field at null infinity are not generally representative of asymptotically flat space--times. We have made a detailed analysis of the constraint equations for ``asymptotically hyperboloidal'' initial data and find that log terms arise generically in asymptotic expansions. These terms are absent in the corresponding Bondi--Sachs--Penrose expansions, and can be related to explicit geometric quantities. We have nevertheless shown that there exists a large class of ``non--generic'' solutions of the constraint equations, the evolution of which leads to space--times satisfying the Bondi--Sachs--Penrose smoothness conditions.