  Gravitational waves from the coalescence of two black holes carry the
signature of the strong field dynamics of binary black holes. In this work we
have used numerical relativity simulations and post-Newtonian theory to
investigate this dynamics. Post-Newtonian theory is a low-velocity expansion
that assumes the companion bodies to be point-particles, while numerical
relativity treats black holes as extended objects with horizons and fully
captures their dynamics. There is a priori no reason for the waveforms computed
using these disparate methods to agree with each other, especially at late
times when the black holes move close to the speed of light. We find,
remarkably, that the leading order amplitudes in post-Newtonian theory agree
well with the full general relativity solution for a large set of spherical
harmonic modes, even in the most dynamical part of the binary evolution, with
only some modes showing distinctly different behavior than that found by
numerical relativity simulations. In particular, modes with spherical harmonic
indices l = m as well as l = 2, m = 1 are least modified from their dominant
post-Newtonian behavior. Understanding the nature of these modes in terms of
the post-Newtonian description will aid in formulating better models of the
emitted waveforms in the strong field regime of the dynamics.
