Black holes: boundaries, interactions and physics

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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.