On the use of evolutionary methods in spaces of Euclidean signature
Student No.:20
Time:13:30-15:05, 10.17/ 10.19/ 10.24/ 10.26/ 10.31/ 11.2/ 11.7
Instructor:István Rácz  
Place:Conference Room 4, Floor 2, Jinchunyuan West Bldg.
Starting Date:2017-10-17
Ending Date:2017-11-16

One of the most striking attribute of general relativity is that geometry is dynamical. The course starts by recalling some of the basics of these evolutionary aspects which inevitably ends up with hyperbolic formulations of Einstein’s theory of gravity. Our main aim is to shown that evolutionary methods do play significant role in spaces of Euclidean signature too. In particular, it is shown that once a clear separation of the evolutionary and constraint equations is done, the constraint expressions satisfy a first order symmetric hyperbolic system regardless whether the ambient Einsteinian space is of Lorentzian or Euclidean signature. Since the seminal observations of Lichnerowicz and York the constraint equations are always referred to as a semilinear elliptic system. It was found recently that the constraints may also form either a parabolic-hyperbolic or a strongly hyperbolic system. Some of the recent developments and application will also be discussed.

Basic knowledge of differential geometry and general relativity.

•Wald R M: General relativity, University of Chicago Press, Chicago (1984)
•Choquet-Bruhat Y: General relativity and Einstein's equations, Oxford University Press (2009)

•Further specific references will be given at each lecture.