Black holes: boundaries, interactions and physics

我们正处于黑洞物理学的黄金时代。来自双星黑洞合并的引力波现在已经被多次观测到，在接下来的几个月里，事件视界望远镜应该会发布第一批位于我们银河系中心的黑洞图像。这种新观测的涌现及其与数值模拟和理论的相互作用正在改变这一领域，因为可以前所未有地探索、测试和验证想法。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。*潜在的想法可以通过一个简单的例子来激发。当月球绕地球运行时，它的引力场会引起潮汐，当潮汐在地球上流动时，水和陆地之间的摩擦会减缓地球的自转速度。反过来，凸起向月球拉回，因此人族的旋转角动量被转化为月球轨道角动量。这种引力耦合的净影响是月球以大约4厘米/年的速度从地球后退。这个过程很好地展示了我们是如何在经典物理学中进行推理的。几何形状(潮汐凸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。有了这些流程的知识，我们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，黑洞本身是时空弯曲的，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，在许多星系中，事情并不像看起来那么可怕。经典推理的某些方面是可以恢复的--尽管有一些有趣和意想不到的曲折。我将开发数学工具来确定地平线几何如何约束近地平线时空的结构，以及反过来，近地平线时空如何管理与环境的相互作用(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。我还将学习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面的数值相对论。然而，在一个小物体(可能是黑洞)坠入或擦过质量黑洞的情况下，人们可以使用微扰理论进行模拟，并在笔记本电脑上运行，而不是在超级计算机上运行。这种相互作用不仅本身具有实际意义，而且还提供了检验和应用近视距理论的极佳范例。

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.