Motivated by the possibility of observing gravitational waves from merging
black holes whose spins are nearly extremal (i.e., 1 in dimensionless units),
we present numerical waveforms from simulations of merging black holes with the
highest spins simulated to date: (1) a 25.5-orbit inspiral, merger, and
ringdown of two holes with equal masses and spins of magnitude 0.97 aligned
with the orbital angular momentum; and (2) a previously reported 12.5-orbit
inspiral, merger, and ringdown of two holes with equal masses and spins of
magnitude 0.95 anti-aligned with the orbital angular momentum. First, we
consider the horizon mass and spin evolution of the new aligned-spin
simulation. During the inspiral, the horizon area and spin evolve in remarkably
close agreement with Alvi's analytic predictions, and the remnant hole's final
spin agrees reasonably well with several analytic predictions. We also find
that the total energy emitted by a real astrophysical system with these
parameters---almost all of which is radiated during the time included in this
simulation---would be 10.952% of the initial mass at infinite separation.
Second, we consider the gravitational waveforms for both simulations. After
estimating their uncertainties, we compare the waveforms to several
post-Newtonian approximants, finding significant disagreement well before
merger, although the phase of the TaylorT4 approximant happens to agree
remarkably well with the numerical prediction in the aligned-spin case. We find
that the post-Newtonian waveforms have sufficient uncertainty that hybridized
waveforms will require far longer numerical simulations (in the absence of
improved post-Newtonian waveforms) for accurate parameter estimation of
low-mass binary systems.Comment: 17 pages, 7 figures, submitted to Classical and Quantum Gravit