|General Relativity and the Nonlinear Memory Effect of Gravitational Waves|
|Time：||13:00-14:50 Tue.; 8:00-9:50 Thu.|
|Instructor：||Lydia Bieri [University of Michigan]|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building|
General relativity is a rich interplay between geometry, analysis and physics. Methods of geometric analysis have proven to be most effective to investigate these structures. This course will start with an introduction into the Cauchy problem in general relativity. Then it will cover null hypersurfaces in Lorentzian spacetimes, establishing the geometric tools to investigate gravitational radiation. After that, I will discuss the nonlinear memory effect of gravitational waves. We will discuss D. Christodoulou's pioneering article of 1991 as well as new results of 2010 and 2011 co-authored by L. Bieri, P. Chen, S.-T. Yau for the case when electromagnetic fields are present.
Knowledge in Riemannian geometry and partial differential equations.
Reference for the course:
References for research articles will be given during the course. In addition, some of the material and background material can be found in the following books:
``General Relativity". R.M. Wald. Univ. Chicago Press. Chicago. (1984).
``Mathematical Problems of GR I". D. Christodoulou. EMS Zurich. (2008).
``Riemannian Geometry and Geometric Analysis". J. Jost. Springer. Berlin Heidelberg. (1998).
``Semi-Riemannian Geometry. With Applications to Relativity". B. O'Neill. Pure and Appl. Math. Academic Press. New York. (1983).