  The final stage of a binary black hole merger is ringdown, in which the
system is described by a Kerr black hole with quasinormal mode perturbations.
It is far from straightforward to identify the time at which the ringdown
begins. Yet determining this time is important for precision tests of the
general theory of relativity that compare an observed signal with quasinormal
mode descriptions of the ringdown, such as tests of the no-hair theorem. We
present an algorithmic method to analyze the choice of ringdown start time in
the observed waveform. This method is based on determining how close the strong
field is to a Kerr black hole (Kerrness). Using numerical relativity
simulations, we characterize the Kerrness of the strong-field region close to
the black hole using a set of local, gauge-invariant geometric and algebraic
conditions that measure local isometry to Kerr. We produce a map that
associates each time in the gravitational waveform with a value of each of
these Kerrness measures; this map is produced by following outgoing null
characteristics from the strong and near-field regions to the wave zone. We
perform this analysis on a numerical relativity simulation with parameters
consistent with GW150914- the first gravitational wave detection. We find that
the choice of ringdown start time of $3\,\mathrm{ms}$ after merger used in the
GW150914 study to test general relativity corresponds to a high dimensionless
perturbation amplitude of $ \sim 7.5 \times 10^{-3}$ in the strong-field
region. This suggests that in higher signal-to-noise detections, one would need
to start analyzing the signal at a later time for studies that depend on the
validity of black hole perturbation theory.
