The non-linear generation of harmonics in gravitational perturbations of
black holes is explored using numerical relativity based on an in-going
light-cone framework. Localised, finite, perturbations of an isolated black
hole are parametrised by amplitude and angular harmonic form. The response of
the black hole spacetime is monitored and its harmonic content analysed to
identify the strength of the non-linear generation of harmonics as a function
of the initial data amplitude. It is found that overwhelmingly the black hole
responds at the harmonic mode perturbed, even for spacetimes with 10% of the
black hole mass radiated. The relative efficiencies of down and up-scattering
in harmonic space are computed for a range of couplings. Down-scattering,
leading to smoothing out of angular structure is found to be equally or more
efficient than the up-scatterings that would lead to increased rippling. The
details of this non-linear balance may form the quantitative mechanism by which
black holes avoid fission even for arbitrary strong distortions.Comment: 13 pages; submitted to Phys. Rev
