ncts

Einstein’s prediction of gravitational waves was only rigorously justified in 1960’s. The work of Bondi and Trautman and their collaborators established the mass loss formula that gave the first nonlinear theoretical verification of gravitational waves. Subsequent work of Penrose and his contemporaries defined the conformal compactification near future null infinity which paved the background for a systematic study of gravitational radiation. The development culminated in the breakthrough in 2015 when gravitational waves were detected by mankind for the first time. While most of the quantitative study in gravitational waves detection rely on numerical methods and the physical theory established earlier, the study of the Cauchy problems of the Einstein equation in the past few decades (in particular, the Christodoulou-Klainerman theory) suggested that the structure of future null infinity is more erratic and irregular than the picture portrayed in the physical theory. Recent progresses in geometry and PDE in mathematics provide powerful and timely tools to reexamine, reinforce, and update the theory. In this minicourse, we will discuss the mathematical theory of gravitational radiation which includes, but not limits to, the Bondi-Trautman mass loss formula, the BMS group, asymptotically hyperboloids, memory effect, the Cauchy formulation of Einstein’s equation, and future null infinity. This minicourse will gather researchers working on the frontier of recent development and aim to provide a sound foundation to work on related areas.