  (Abridged) We study the dynamical evolution of a stationary, axisymmetric,
and perfectly conducting cold accretion disk containing a large-scale magnetic
field around a Kerr black hole, trying to understand the relation between
accretion and the transportation of angular momentum and energy. We solve the
radial momentum equation for solutions corresponding to an accretion flow that
starts from a subsonic state at infinity, smoothly passes the fast critical
point, then supersonically falls into the horizon of the black hole. The
solutions always have the following features: 1) The specific energy of fluid
particles remains constant but the specific angular momentum is effectively
removed by the magnetic field. 2) At large radii, where the disk motion is
dominantly rotational, the energy density of the magnetic field is
equipartitioned with the rotational energy density of the disk. 3) Inside the
fast critical point, where radial motion becomes important, the ratio of the
electromagnetic energy density to the kinetic energy density drops quickly. The
results indicate that: 1) Disk accretion does not necessarily imply energy
dissipation since magnetic fields do not have to transport or dissipate a lot
of energy as they effectively transport angular momentum. 2) When resistivity
is small, the large-scale magnetic field is amplified by the shearing rotation
of the disk until the magnetic energy density is equipartitioned with the
rotational energy density, ending up with a geometrically thick disk. This is
in contrast with the evolution of small-scale magnetic fields where if the
resistivity is nonzero the magnetic energy density is likely to be
equipartitioned with the kinetic energy density associated with local random
motions (e.g., turbulence), making a thin Keplerian disk possible.
