Black holes: boundaries, interactions and physics

我们正处于黑洞物理学的黄金时代。现在已经多次观察到二元黑洞合并产生的引力波，在接下来的几个月内，事件视界望远镜应该会发布我们银河系中心黑洞的第一张图像。这种新的观测及其与数值模拟和理论的相互作用正在改变这个领域，因为思想可以前所未有地被探索，测试和验证。我的研究计划的主要目标是开发新的数学工具，以更好地解释这些数值和理论结果。 一个简单的例子可以激发出这个基本思想。当月球绕地球运行时，它的引力场会引起潮汐，当它们绕着地球仪流动时，水和陆地之间的摩擦会减缓地球的自转。这些凸起反过来又拉住了月球，于是地球的旋转角动量就转化成了月球轨道的角动量。这种引力耦合的净效应是月球以每年约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（潮汐隆起的形状和到月球的轨道距离）与引力场相互作用，并驱动能量和角动量的转移。了解了这些流动，我们就觉得我们理解了这个系统。 涉及黑洞的相互作用更为复杂。牛顿引力场被时空几何所取代，不再以简单的方式叠加。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。此外，黑洞本身就是时空曲率，没有明确的方法将它们与环境分开。牛顿物理推理的基础似乎已经丧失。 我的研究将研究动态黑洞和相互作用，并表明在许多情况下，事情并不像它们看起来那么可怕。古典推理的某些方面可以被恢复--尽管会有有趣和意想不到的曲折。我将开发数学工具来确定视界几何如何约束近视界时空的结构，以及近视界时空如何控制与环境的相互作用（包括引力波发射）。清楚地理解这种结构将发展直觉，并有助于解释物理过程。我还将研究极端质量比相互作用的物理学。一般来说，模拟黑洞合并需要全尺度的数值相对论。然而，在一个小物体（可能是一个黑洞）陷入或擦过一个大质量黑洞的情况下，人们可以使用微扰理论进行模拟，并在笔记本电脑而不是超级计算机上运行它们。这种相互作用不仅本身具有物理意义，而且为检验和应用近视界理论提供了极好的例子。

We are in a golden age of black hole physics. Gravitational waves from binary black hole mergers have now been observed multiple times and within the next few months the Event Horizon Telescope should release the first images of the black hole at the centre of our galaxy. This rush of new observations and its interaction with numerical simulations and theory is changing the field as ideas can be probed, tested and verified as never before. The main goal of my research program is to develop new mathematical tools to better interpret those numerical and theoretical results. The underlying idea can be motivated by a simple example. As the moon orbits the Earth, its gravitational field raises tides and, as they flow around the globe, friction between the water and land slows the Earth's rotation. In turn the bulges pull back on the moon and so terran rotational angular momentum is transformed into lunar orbital angular momentum. The net effect of this gravitational coupling is that the moon recedes from the Earth at a rate of about 4cm/year. This process nicely demonstrates how we reason in classical physics. Geometry (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. With a knowledge of these flows, we feel that we understand the system. Interactions involving black holes are more complicated. Newtonian gravitational fields are replaced by spacetime geometry and no longer superpose in a simple way. 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. Further, black holes are themselves spacetime curvature and there is no clear way to separate them from their environment. The foundations of Newtonian physical reasoning appear to be lost. My research will study dynamic black holes and interactions and show that, in many regimes, things are not as dire as they appear. Aspects of classical reasoning can be recovered - though with interesting and unexpected twists. I will develop mathematical tools to determine how horizon geometry constrains the structure of the near-horizon spacetime and how, in turn, that near-horizon spacetime governs interactions with the environment (including gravitational wave emissions). Clearly understanding this structure will develop intuition and help interpret physical processes. I will also study the physics of extreme-mass ratio interactions. In general, simulating black hole mergers requires full scale numerical relativity. However, in cases where a small object (maybe a black hole) either plunges into or grazes a massive black hole, one can do the simulations using perturbation theory and run them on laptops rather than supercomputers. Such interactions are not only of physical interest in their own right but also provide excellent examples to test and apply the near-horizon theory.