\over R^8} -{2327 \over 19200} {M^9 \over R^9} \right)
\nonumber \\
& & +{7 P^2 M (M+12R)(M+2R)^2(\ln(2M)-\ln(M+2R)) \over 40 R^3 (M^2+10MR+4R^2)}.\end{aligned}$$

Physical validity of the perturbative treatment
-----------------------------------------------

Inspecting the initial data for the Zerilli function one finds that it behaves in a non-conventional way. Here is where we note significant differences with the case of single spinning holes [@GlNiPrPuboyo].

The first unusual thing one notices is that the initial data goes asymptotically to a constant value for $R\rightarrow\infty$. This is different from the data for the “close limit” of two black holes (momentarily stationary or boosted) where the Zerilli function goes to zero at infinity. The root of this problem can be traced down to the falloff conditions of the extrinsic curvature. In all other cases in which the “close limit” approximation has been applied, the extrinsic curvature falls off as $1/r^3$ at infinity. For the case in this paper, it decreases as $1/r^2$ (otherwise the momentum would vanish). This, in particular, leads to falloff conditions in the gauge vectors we use to eliminate the $\ell=1$ even pieces of the extrinsic curvature. In turn, the falloff condition of the gauge vectors influences, via the quadratic terms in the second 