Numerical studies of solutions to Equations (16) – (17) indicate that for most spatial points, behavior
similar to that described by the asymptotic expansions (37) – (38) occurs [11, 10]. However, the studies also
indicate that there are exceptional spatial points at which the behavior is different. Due to the appearance
of the solutions in the neighborhood of the exceptional points, the corresponding features have been referred
to as “spiky features” or “spikes”. Their existence would seem to necessitate an understanding of
the “spikes” on an analytical level in order to be able to describe the asymptotics of general
T^{3}-Gowdy solutions. An important step in this direction was achieved by demonstrating the
existence of a large class of solutions to Equations (16) – (17) with spikes [71]. In order to be
able to describe these solutions, we need to introduce some transformations taking solutions to
solutions.

9.1 Inversion

9.2 Gowdy to Ernst transformation

9.3 False spikes

9.3.1 True spikes

9.4 High velocity spikes

9.2 Gowdy to Ernst transformation

9.3 False spikes

9.3.1 True spikes

9.4 High velocity spikes

http://www.livingreviews.org/lrr-2010-2 |
This work is licensed under a Creative Commons License. Problems/comments to |