Studies of Singularities and Black Holes

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，我们想知道对于整个不完全观测者，曲率如何沿着他们的世界线运动，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，PI打算对具有奇点的时空进行数值研究来解决这些问题。PI已经开发并成功地应用了一个完全三维空间的真空代码来研究宇宙学奇点，并为振荡奇点的BKL图像找到了支持。他计划通过进一步的工作来补充这一点，包括物质来源，以测试大爆炸附近“物质不重要”的想法。PI还将研究坐标条件如何影响碰撞黑洞的数值演化。

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 for 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, the PI intends to perform numerical studies of spacetimes with singularities to address these issues. The PI has already developed and successfully applied a fully 3-space dimensional vacuum code to study cosmological singularities and has found support for the BKL picture of oscillatory singularities. He plans to complement this with further work involving matter sources to test the idea that "matter doesn't matter" near the big bang. The PI also will study how coordinate conditions effect the numerical evolution of colliding black holes.