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Gravitational waves are one of the most important diagnostic tools in theanalysis of strong-gravity dynamics and have been turned into an observationalchannel with LIGO's detection of GW150914. Aside from their importance inastrophysics, black holes and compact matter distributions have also assumed acentral role in many other branches of physics. These applications ofteninvolve spacetimes with $D>4$ dimensions where the calculation of gravitationalwaves is more involved than in the four dimensional case, but has now becomepossible thanks to substantial progress in the theoretical study of generalrelativity in $D>4$. Here, we develop a numerical implementation of theformalism by Godazgar and Reall (Ref.[1]) -- based on projections of the Weyltensor analogous to the Newman-Penrose scalars -- that allows for thecalculation of gravitational waves in higher dimensional spacetimes withrotational symmetry. We apply and test this method in black-hole head-oncollisions from rest in $D=6$ spacetime dimensions and find that a fraction$(8.19\pm 0.05)\times 10^{-4}$ of the Arnowitt-Deser-Misner mass is radiatedaway from the system, in excellent agreement with literature results based onthe Kodama-Ishibashi perturbation technique. The method presented herecomplements the perturbative approach by automatically including contributionsfrom all multipoles rather than computing the energy content of individualmultipoles.

Gravitational wave extraction in higher dimensional numerical relativity using the Weyl tensor