  Fragmentation of highly differentially rotating massive stars that undergo
collapse has been suggested as a possible channel for binary black hole
formation. Such a scenario could explain the formation of the new population of
massive black holes detected by the LIGO/VIRGO gravitational wave laser
interferometers. We probe that scenario by performing general relativistic
magnetohydrodynamic simulations of differentially rotating massive stars
supported by thermal radiation pressure plus a gas pressure perturbation. The
stars are initially threaded by a dynamically weak, poloidal magnetic field
confined to the stellar interior. We find that magnetic braking and turbulent
viscous damping via magnetic winding and the magnetorotational instability in
the bulk of the star redistribute angular momentum, damp differential rotation
and induce the formation of a massive and nearly uniformly rotating inner core
surrounded by a Keplerian envelope. The core + disk configuration evolves on a
secular timescale and remains in quasi-stationary equilibrium until the
termination of our simulations. Our results suggest that the high degree of
differential rotation required for $m=2$ seed density perturbations to trigger
gas fragmentation and binary black hole formation is likely to be suppressed
during the normal lifetime of the star prior to evolving to the point of
dynamical instability to collapse. Other cataclysmic events, such as stellar
mergers leading to collapse, may therefore be necessary to reestablish
sufficient differential rotation and density perturbations to drive
nonaxisymmetric modes leading to binary black hole formation.
