2 research outputs found
Smooth Gowdy symmetric generalized Taub-NUT solutions
We study a class of S3 Gowdy vacuum models with a regular past Cauchy horizon
which we call smooth Gowdy symmetric generalized Taub-NUT solutions. In
particular, we prove existence of such solutions by formulating a singular
initial value problem with asymptotic data on the past Cauchy horizon. The
result of our investigations is that a future Cauchy horizon exists for generic
asymptotic data. Moreover, we derive an explicit expression for the metric on
the future Cauchy horizon in terms of the asymptotic data on the past horizon.
This complements earlier results about S2xS1 Gowdy models.Comment: 56 pages, 1 figure. The new version contains a detailed explanation
of the Fuchsian method on the 2-spher
Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes
We set up the singular initial value problem for quasilinear hyperbolic
Fuchsian systems of first order and establish an existence and uniqueness
theory for this problem with smooth data and smooth coefficients (and with even
lower regularity). We apply this theory in order to show the existence of
smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein
equations, which exhibit AVTD (asymptotically velocity term dominated) behavior
in the neighborhood of their singularities and are polarized or half-polarized.Comment: 78 page