  Gravitational waves from the explosive merger of distant black holes are
encoded with details regarding the complex extreme-gravity spacetime present at
their source. Famously described by the Kerr spacetime metric for rotating
black holes in general relativity, what if effects beyond this theory are
present? One way to efficiently test this hypothesis is to first obtain a
metric which parametrically deviates from the Kerr metric in a
model-independent way. Given such a metric, one can then predict the ensuing
corrections to both the inspiral and ringdown portions of the gravitational
waveform for black holes present in the new spacetime. With these tools in
hand, one can then test gravitational wave signals for such effects by two
different methods, (i) inspiral-merger-ringdown consistency test, and (ii)
parameterized test. In this paper, we demonstrate the exact recipe one needs to
do just this. We first derive parameterized corrections to the waveform
inspiral, ringdown, and remnant properties for a generic non-Kerr spacetime and
apply this to two example beyond-Kerr spacetimes each parameterized by a single
non-Kerr parameter. We then predict the beyond-Kerr parameter magnitudes
required in an observed gravitational wave signal to be statistically
inconsistent with the Kerr case in general relativity. We find that the two
methods give very similar bounds. The constraints found with existing
gravitational-wave events are comparable to those from x-ray observations,
while future gravitational-wave observations using Cosmic Explorer (Laser
Interferometer Space Antenna) can improve such bounds by two (three) orders of
magnitude.
