4 research outputs found
The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion
We show that for -symmetric spacetimes on a constant of
motion associated with the well known Geroch transformation, a functional
, quadratic in gravitational momenta, is strictly positive
in an open subset of the set of all -symmetric initial data, and
therefore not weakly zero. The Mixmaster initial data appear to be on the
boundary of that set. We calculate the constant of motion perturbatively for
the Mixmaster spacetime and find it to be proportional to the minisuperspace
Hamiltonian to the first order in the Misner anisotropy variables, i.e. weakly
zero. Assuming that is exactly zero for the Mixmaster spacetime, we show
that Geroch's transformation, when applied to the Mixmaster spacetime, gives a
new \mbox{-symmetric} solution of the vacuum Einstein equations, globally
defined on \mbox{},which is non-homogeneous and
presumably exhibits Mixmaster-like complicated dynamical behavior.Comment: 25 pages, preprint YCTP-20-93, Revte
Asymptotic Behavior of the Gowdy Spacetimes
We present new evidence in support of the Penrose's strong cosmic censorship
conjecture in the class of Gowdy spacetimes with spatial topology.
Solving Einstein's equations perturbatively to all orders we show that
asymptotically close to the boundary of the maximal Cauchy development the
dominant term in the expansion gives rise to curvature singularity for almost
all initial data. The dominant term, which we call the ``geodesic loop
solution'', is a solution of the Einstein's equations with all space
derivatives dropped. We also describe the extent to which our perturbative
results can be rigorously justified.Comment: 30 page