a \over 128 R^3} 
\label{misnerbound}\end{aligned}$$ Notice that $\phi^{(2)}_2(R)$ falls off only as $R^{-2}$ for large $R$.

For completeness, we also present the solution one obtains if one chooses the “puncture” boundary condition considered by Brandt and Brügmann [@BrBr] recently, $$\begin{aligned}
 \phi^{(2)}_0(R) &=&
{\frac {{M}^{4}+10\,{M}^{3}R+40\,{M}^{2}{R}^{2}+80
\,M{R}^{3}+80\,{R}^{4}}{8\,M\left (2\,R+M\right )^{
5}}} \label{brbrbrbr}\\
 \phi^{(2)}_2(R) &=&{\frac {120\,{R}^{5}+768\,{R}^{4}M+1078\,{R}^{3}{M}
^{2}+658\,{R}^{2}{M}^{3}+189\,R{M}^{4}+21\,{M}^{5}}
{20\,{R}^{2}\left (2\,R+M\right )^{5}}}\\
&&-21{\frac {
\left (\ln (2\,R+M)-\ln (M)\right )M}{40\,
{R}^{3}}}\nonumber\end{aligned}$$ but we will only consider the solution (\[misnerbound\]) in the rest of this paper.

To obtain an initial data set appropriate for a perturbative evolution we proceed as follows. First, in an ADM type decomposition, we choose our shift functions $N_a=0$, so that we have,

$$\begin{aligned}
\label{ADMeqs}
ds^2 & = & g_{ab} dx^a dx^b - N^2 (dt)^2 \nonumber \\
{\partial g_{ab} \over \partial t} & = & -2NK_{ab}\end{aligned}$$

Next, we assume that on our initial slice, at $t=0$, the 3-metric $g_{ab}$ and extrinsic curvature $K_{ab}$ are given by the above conformal flatness construction. Namely, we have $g_{ab}=\phi^4 \delta_{ab}$ and $K_{ab}=\phi^{-2} \widehat{K}_{ab} $, with $\widehat{K}_{ab}$ given by (\[Ksphe\]), and $\phi$ given by (\[eqphi\]). (This, of course, ensures that our initial data satisfies the constraint equations). We next change from the conformal spherical radial coordinates $R$, to a 