Black holes and their boundaries: from equilibrium properties to how dynamical black holes interact with their environment

当月球绕地球运行时，它的引力场会引起潮汐。当潮汐在全球范围内膨胀时，水和陆地之间的摩擦减慢了地球的自转。同时，凸起的引力场对月球产生拉回作用，于是人类的旋转角动量转化为月球轨道角动量。正如在任何涉及摩擦的问题中一样，能量被耗散，这种引力耦合的净效应是月球以每年近4厘米的速度远离地球。这个过程很好地展示了我们如何在经典物理学中进行推理。几何形状（在这种情况下是潮汐隆起的形状和到月球的轨道距离）与引力场相互作用，并驱动系统周围能量和角动量的转移。一旦我们知道了力、能量和动量的流动，我们就觉得我们理解了这个系统。

As the moon orbits the Earth, its gravitational field raises the tides. As the tidal bulges flow around the globe, friction between the water and land slows the Earth's rotation. At the same time, the gravitational field of the bulges pulls back on the moon and so terran rotational angular momentum is transformed into lunar orbital angular momentum. As in any problem involving friction, energy is dissipated and a net effect of this gravitational coupling is that the moon recedes from the Earth at a rate of almost 4cm/year. This process nicely demonstrates how we reason in classical physics. The geometry (in this case the shape of the tidal bulge and orbital distance to the moon) interacts with the gravitational field and drives a transfer of energy and angular momentum around the system. Once we know about the forces and the flows of energy and momentum, we feel that we understand the system. Interactions involving black holes are a lot more complicated. By definition, black hole physics involves incredibly strong gravitational fields. Then the gravitational fields of Newtonian physics are replaced by the spacetime geometry of general relativity and no longer superpose in a simple way. Furthermore, close to the black hole we can no longer rely on energy and momentum to build intuition: their conservation laws come from symmetries that no longer exist. To make matters even more confusing, there is not even universal agreement on how to define the boundary of a dynamical black hole. The foundations of classical physical reasoning appear to be lost. A primary focus of this research program will be the study of dynamic black holes and how they interact with their enviroment. In many circumstances, including most astrophysical processes, things are not as dire as they might first appear and many aspects of classical reasoning can be recovered - though with interesting and unexpected twists. I will develop mathematical tools to aid in the understanding of real astrophysical events as well as some more esoteric problems involving higher dimensions, unexpected dualities and other exotica.