Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Explore a lecture on massive waves gravitationally bound to static bodies, delivered by Ethan Sussman at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the intriguing world of astrophysical spacetimes and wave equations, examining the behavior of solutions to the massless wave equation and the Klein-Gordon equation on various spacetime models. Discover why solutions decay over time in certain scenarios, but not in static spacetimes with asymptotically conic manifolds. Learn about the existence of infinitely many standing wave solutions with Schwartz initial data on specific spacetimes. Investigate topics such as the Clan Gordon equation, decay rates, asymptotically curved spacetimes, nontrapping conditions, and the construction of standing wave solutions. Gain insights into the theoretical aspects, including bump functions and discrete spectrum, as part of the Thematic Programme on "Spectral Theory and Mathematical Relativity."