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。当潮汐隆起绕着地球仪流动时，水和陆地之间的摩擦减缓了地球的自转。与此同时，凸起的引力场会拉回月球，因此地球的旋转角动量会转化为月球轨道的角动量。与任何涉及摩擦的问题一样，能量被耗散，这种引力耦合的净效应是月球以每年近4厘米的速度从地球后退。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，并驱动系统周围的能量和角动量转移。一旦我们了解了力和能量与动量的流动，我们就觉得我们理解了这个系统。涉及黑洞的相互作用要复杂得多。根据定义，黑洞物理学涉及令人难以置信的强大引力场。然后，牛顿物理学的引力场被广义相对论的时空几何所取代，不再以简单的方式叠加。此外，在黑洞附近，我们不能再依靠能量和动量来建立直觉：它们的守恒定律来自不再存在的对称性。更令人困惑的是，关于如何定义动态黑洞的边界，甚至没有普遍的共识。古典物理推理的基础似乎已经丧失。该研究计划的主要重点是研究动态黑洞以及它们如何与环境相互作用。在许多情况下，包括大多数天体物理过程，事情并不像它们最初看起来那么可怕，经典推理的许多方面都可以恢复-尽管有有趣和意想不到的曲折。我将开发数学工具，以帮助理解真实的天体物理事件，以及一些涉及更高维度，意外的对偶和其他新奇的更深奥的问题。

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.