Theorem 6 Consider a solution to Equations (11)–(12
). Let
and let
be the metric induced by the Riemannian metric
given by Equation (22
). Then there is
a
, a
and a curve
such that
for all . The possibilities for
are as follows.
Furthermore, it is possible to describe in detail the behavior of the solutions along the circles; see [75,
Theorem 1.3–1.5, pp. 662–664] as well as [75
, Figure 1.1–1.3, pp. 663–664]. In fact, the solution tends to
the boundary along the circle when
and
,
and
are not all equal to zero. In
the case of
, the solution oscillates around the circle forever and is asymptotically periodic
with respect to a logarithmic time coordinate.
http://www.livingreviews.org/lrr-2010-2 |
Living Rev. Relativity 13, (2010), 2
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