  We perform magnetohydrodynamic simulations of accreting, equal-mass binary
black holes in full general relativity focusing on the impact of black hole
spin on the dynamical formation and evolution of minidisks. We find that during
the late inspiral the sizes of minidisks are primarily determined by the
interplay between the tidal field and the effective innermost stable orbit
around each black hole. Our calculations support that a minidisk forms when the
Hill sphere around each black hole is significantly larger than the black
hole's effective innermost stable orbit. As the binary inspirals, the radius of
the Hill sphere decreases, and minidisk sconsequently shrink in size. As a
result, electromagnetic signatures associated with minidisks may be expected to
gradually disappear prior to merger when there are no more stable orbits within
the Hill sphere. In particular, a gradual disappearance of a hard
electromagnetic component in the spectrum of such systems could provide a
characteristic signature of merging black hole binaries. For a binary of given
total mass, the timescale to minidisk "evaporation" should therefore depend on
the black hole spins and the mass ratio. We also demonstrate that accreting
binary black holes with spin have a higher efficiency for converting accretion
power to jet luminosity. These results could provide new ways to estimate black
hole spins in the future.
