Furthermore, in the polarized case, the integrand appearing on the left-hand side of Equation (58) is
unbounded as
. In fact, the best bound for the integrand is
due to Equation (52
). On the
other hand, the integral is conserved. Moreover, since this conserved quantity determines the overall
behavior of the solution, it is clear that the problem of analyzing the asymptotics numerically is not trivial.
The same phenomenon appears in the nonpolarized case. However, it is of interest to note that the reason
why the mathematical analysis is possible is in part due to the difference in decay rates between
and
http://www.livingreviews.org/lrr-2010-2 |
Living Rev. Relativity 13, (2010), 2
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