论文标题
无所不知的叶子和宇宙学的几何形状
Omniscient foliations and the geometry of cosmological spacetimes
论文作者
论文摘要
我们通过及时曲线在时空（m，g）上识别某些一般的几何条件，这将阻碍无效线的存在，尤其是（M，G）具有紧凑的Cauchy hypersurface。反过来，在巴特尼克（Bartnik）的分裂猜想的背景下，没有这种线条对宇宙学的几何形状产生了众所周知的限制。由于（非）无效线的存在实际上是一个形式不变的特性，因此这种条件只需要申请G的某些合格重新缩放。
We identify certain general geometric conditions on a foliation of a spacetime (M,g) by timelike curves that will impede the existence of null geodesic lines, especially if (M,g) possesses a compact Cauchy hypersurface. The absence of such lines, in turn, yields well-known restrictions on the geometry of cosmological spacetimes, in the context of Bartnik's splitting conjecture. Since the (non)existence of null lines is actually a conformally invariant property, such conditions only need to apply for some suitable conformal rescaling of g.
