  As 2 black holes bound to each other in a close binary approach merger their
inspiral time becomes shorter than the characteristic inflow time of
surrounding orbiting matter. Using an innovative technique in which we
represent the changing spacetime in the region occupied by the orbiting matter
with a 2.5PN approximation and the binary orbital evolution with 3.5PN, we have
simulated the MHD evolution of a circumbinary disk surrounding an equal-mass
non-spinning binary. Prior to the beginning of the inspiral, the structure of
the circumbinary disk is predicted well by extrapolation from Newtonian
results. The binary opens a low-density gap whose radius is roughly two binary
separations, and matter piles up at the outer edge of this gap as inflow is
retarded by torques exerted by the binary; nonetheless, the accretion rate is
diminished relative to its value at larger radius by only about a factor of 2.
During inspiral, the inner edge of the disk at first moves inward in
coordination with the shrinking binary, but as the orbital evolution
accelerates, the rate at which the inner edge moves toward smaller radii falls
behind the rate of binary compression. In this stage, the rate of angular
momentum transfer from the binary to the disk slows substantially, but the net
accretion rate decreases by only 10-20%. When the binary separation is tens of
gravitational radii, the rest-mass efficiency of disk radiation is a few
percent, suggesting that supermassive binary black holes in galactic nuclei
could be very luminous at this stage of their evolution. If the luminosity were
optically thin, it would be modulated at a frequency that is a beat between the
orbital frequency of the disk's surface density maximum and the binary orbital
frequency. However, a disk with sufficient surface density to be luminous
should also be optically thick; as a result, the periodic modulation may be
suppressed.
