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This is the first in a series of papers that investigate the properties ofaccretion flows in the Kerr metric through three-dimensional, generalrelativistic magnetohydrodynamic simulations of tori with a near-Keplerianinitial angular velocity profile. We study four models with increasing blackhole spin, from a/M=0 to 0.998, for which the structural parameters of theinitial tori are maintained nearly constant. The subsequent accretion flowsarise self-consistently from stresses and turbulence created by themagnetorotational instability. We investigate the overall evolution and thelate-time global structure in the resulting non-radiative accretion flows,including the magnetic fields within the disks, the properties of the flow inthe plunging region, and the flux of conserved quantities into the black hole.Independent of black hole spin, the global structure is described in terms offive regions: the main disk body, the coronal envelope, the inner disk,consisting of an inner torus and plunging region, an evacuated axial funnel,and a bi-conical outflow confined to the corona-funnel boundary. We findevidence for lower accretion rates, stronger funnel-wall outflows, andincreased stress in the near hole region with increasing black hole spin.

Magnetically Driven Accretion Flows in the Kerr Metric. I. Models and Overall Structure