The Physics of black holes and their environments: consequences for gravitational wave science

Ten short years ago, we had the rare privilege of witnessing the onset of a renaissance in science: humanity finally succeeded in its arduous quest to directly detect gravitational waves. This breakthrough did not occur in a vacuum: it was the natural culmination of decades of research dedicated towards understanding the nature of gravitation based on Einstein's General Theory of Relativity. It is a story of false starts, perseverance, and remarkable insights, propelled as much by technological progress as by human curiosity. We now proudly live in the new golden age of gravitational physics. The detection of gravitational wave signals from the merger of binary black holes and neutron stars are becoming routine. Coupled with our theoretical understanding of phenomena in the strong gravity regime, black hole physics has become a precision science. The purpose of these lecture notes is to help the reader understand the language and framework of this rapidly evolving subject, and to develop the ability to interpret, think, and discuss ideas that lie at the confluence of gravitational wave astronomy and black hole physics. It is our hope that these notes will prepare students and colleagues for the next revolution when gravitational wave events become commonplace and we begin to observe unexpected features in the signal, indicating either surprising astrophysical scenarios or a strong need to modify the theoretical description of gravitational interactions. We provide first principles analysis of black hole and gravitational wave physics, and sometimes a very personal interpretation of results. We share with the readers a number of notebooks that will allow them to reproduce some of the most important results in the field, and could even help in carrying out state-of-the-art research. We also include a few original results that we think are helpful in understanding the broader picture.