Studies of Singularities and Black Holes

奇点定理告诉我们奇点形成于大量时空，包括大爆炸和恒星引力坍缩形成黑洞等物理上相关的情况。然而，这些定理几乎没有告诉我们奇点的本质。例如，我们想知道对于所有的不完全观察者，曲率是如何沿着他们的世界线运动的，以及他们是否能在到达奇点之前看到奇点。由于我们没有封闭形式的爱因斯坦方程的通解，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全三维空间真空码来研究宇宙奇点，并为BKL振荡奇点图找到了支持。他计划用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“物质无关紧要”的观点。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.