The synergy between numerical and perturbative approaches to Black holes.

When I started graduate school, I began a thesis project in perturbation theory of spherical spacetimes. I still remember well how my advisor, Vincent Moncrief, an expert in perturbation theory, advised me to study a paper by Vishveshwara on black hole perturbations [1]. “That’s the best place to find the perturbation formalism”, he told me. At that time, of course, I had no idea how important this subject would continue to be years later. I was very lucky to become grounded in this subject at an “early age”, and I knew it would provide important insight into problems that were intractable in numerical relativity at that time. However I did not appreciate that even as numerical relativity would become more and more mature, harnessing hundreds of processors in parallel to solve ever larger problems, perturbation theory would continue to play such an important role in so many ways. In fact, its role in numerical relativity has become even more important in recent years, as I describe below. Vishu’s work in this area influenced me in ways that I appreciate even more as my own research moves into large scale numerical simulation.