Events

Date: 29 October 2024   Time: 14:00 - 15:00

In this talk we will start by reviewing the structure of some model spacetimes containing closed timelike
curves (CTCs) such as Misner space, and spacetimes with moving or rotating cosmic strings. In general such
spacetimes contain both a chronal and non-chronal region separated by a "chronology horizon". We give initial data for the wave equation on a partial Cauchy surface in the chronal region and show that the Cauchy
problem is well-posed up to and on the chronology horizon. We then consider extending the solution beyond
the chronology horizon. In the model spacetimes we can first pass to an covering space and then introduce
coordinates so that the identifying isometries are manifest in one periodic coordinate. Factoring out this
coordinate we obtain a reduction of the wave equation which turns out to be of mixed type, changing from
hyperbolic to elliptic on the horizon. The well-posedness of the solution then turns out to be similar to that
of the classical Tricomi problem which is also a PDE which changes type on a hypersurface. We end by
discussing the situation in more general spacetimes.