RUI: Studies of Singularities

奇点定理告诉我们，奇点形成于一大类时空中，包括大爆炸和星星引力坍缩形成黑洞的物理相关情形。 然而，这些定理很少告诉我们关于奇点的性质。 例如，我们想知道不完全观测者的整个类别，曲率如何沿着他们的世界线表现，以及他们是否能在撞到奇点之前看到奇点。由于我们没有爱因斯坦方程的封闭形式的通解，因此建议使用所有可用于研究奇点的方法：（i）找到精确解并研究它们的奇点，（ii）以一般的方式研究奇异时空类的行为，或者（iii）对具有奇点的时空进行数值研究以解决这些问题。 （1/2）

The singularity theorems tell us that singularities form in a large class of spacetimes, including the physically relevant cases of the big bang and of the gravitational collapse of a star to form a black hole. However, these theorems tell us very little about the nature of the singularities. For example, we would like to know the entire class of incomplete observers, how the curvature behaves along their world lines and whether they can see the singularity before they hit it. Since we do not have the general solution of Einstein's equation in closed form, it is proposed to use all the methods available for the study of singularities: (i) to find exact solutions and study their singularities, (ii) to examine, in a general way the behavior of classes of singular spacetimes, or (iii) to perform a numerical study of spacetimes with singularities to address these issues. ½¼^¡&ú¼^¼(½