SINGULARITIES OF GRAVITATIONAL COLLAPSE AND COSMOLOGY
SINGULARITIES OF GRAVITATIONAL COLLAPSE AND COSMOLOGY
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DOI：
10.1098/rspa.1970.0021
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发表时间：
1970-01-01
影响因子：
--
通讯作者：
PENROSE, R
中科院分区：
文献类型：
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作者：
HAWKING, SW;PENROSE, R
提出了一个关于时空奇异性的新定理，该定理在很大程度上吸收和推广了以前已知的结果。该定理意味着，如果宇宙在空间上是封闭的，或者存在一个经历相对论引力坍缩的“物体”（存在一个被捕获的表面），或者存在一个点p，其过去的零锥遇到足够的物质，使得通过p的零射线的发散在p的过去的某个地方改变符号（i），那么时空奇点是可以预期的。e.对于给定尺寸的小物体，从上看，有一个最小的视立体角。该定理适用于以下四个物理假设：（一）爱因斯坦方程成立（2）能量密度不小于负的每一个主压，也不小于负的三个主压之和（“能量条件”），（iii）没有封闭的类时曲线，（iv）每一个类时或零测地线进入一个区域，其中曲率不是专门与测地线对齐。(This最后一个条件在任何足够一般的物理现实模型中都成立。）与以前的结果一样，这里使用类时或零测地线不完全性作为时空奇点存在的指示。本定理不需要关于整体柯西超曲面存在性的假设。
A new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results. The theorem implies that space-time singularities are to be expected ifeitherthe universe is spatially closedorthere is an ‘object’ undergoing relativistic gravitational collapse (existence of a trapped surface)orthere is a pointpwhose past null cone encounters sufficient matter that the divergence of the null rays throughpchanges sign somewhere to the past ofp(i. e. there is a minimum apparent solid angle, as viewed frompfor small objects of given size). The theorem applies if the following four physical assumptions are made: (i) Einstein’s equations hold (with zero or negative cosmological constant), (ii) the energy density is nowhere less than minus each principal pressure nor less than minus the sum of the three principal pressures (the ‘energy condition’), (iii) there are no closed timelike curves, (iv) every timelike or null geodesic enters a region where the curvature is not specially alined with the geodesic. (This last condition would hold in any sufficiently general physically realistic model.) In common with earlier results, timelike or null geodesic incompleteness is used here as the indication of the presence of space-time singularities. No assumption concerning existence of a global Cauchy hypersurface is required for the present theorem.