Explore the fourth installment of Alexander Strohmaier's lecture series on the spectral theory of stationary spacetimes, delivered as part of the Thematic Programme on "Spectral Theory and Mathematical Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into advanced concepts in mathematical physics and relativity theory during this one-hour talk, which took place between June 5 and July 28, 2023. Gain insights into the intricate relationship between spectral theory and the mathematical description of stationary spacetimes, furthering your understanding of this complex field of study.