Bowen–York hole to a boosted Schwarzschild black hole. The results for the energy can be summarized by a simple formula which, to leading order in $P$ reads, $$\left({E_{\rm radiated} \over M_{ADM}}\right) = 4.1 \times 10^{-2} 
\left({P\over M_{ADM}}\right)^{4}$$ where the prefactor was computed numerically [^2].

Figure \[fig1\] shows the radiated energy as a function of the momentum. We see that for values of the momentum close to $P/M_{ADM}\sim 0.4$ the total radiated energy by the “relaxation” of a single boosted Bowen–York black hole to a Schwarzschild black hole is similar to the total radiated energy in a close limit collision of Bowen–York black holes [@GlNiPrPuboost2] and figure \[fig2\]. One could therefore be tempted to say that for values of $P/M_{ADM} > 0.4$ one should stop using these families of initial data. A puzzling element is that we have already evolved these families of initial data in collision situations and compared with actual non-linear integrations of the Einstein equations [@boost1; @GlNiPrPuboost2] and [*we know*]{} that these families of initial data radiate less in collisions than the values we are predicting here for each individual hole, at least for close separations. The results for these collisions are recollected in figure \[fig2\].

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