leading order. The energy, being quadratic in the fields, will generically contain terms that behave like $L^4$, $P^2
L^2$ and $P^4$, the latter being the terms we encountered in this paper. However, the top collision contains terms $L^4$, $P L^3$ and $P^2 L^2$, as discussed in reference [@GlNiPrPuboost2] (the extrinsic curvature goes as $PL$ and the conformal factor as $L^2$ at leading order). Therefore if one were to consider “close” black holes and were to consider the radiated energy as a function of $P$, as we have done above, one would encounter that the perturbative predictions —at the order considered— will differ significantly as soon as the $P^4$ terms start to grow. The moral from this paper insofar as the choice of the origin is: perturbation theory breaks down quickly as a function of momentum for situations with net linear momentum, it is best to analyze collisions set up in the center-of-momentum frame.

As expected, given the nature of the Zerilli equation, the waveforms that one obtains from the “relaxation” just behave like quasinormal ringing. Figure \[fig4\] shows the waveform of the decay. The form is that of a typical ringdown, and it therefore takes an amount of time of 