  Black holes with accretion rates well below the Eddington rate are expected
to be surrounded by low-density, hot, geometrically thick accretion disks. This
includes the two black holes being imaged at sub-horizon resolution by the
Event Horizon Telescope. In these disks, the mean free path for Coulomb
interactions between charged particles is large, and the accreting matter is a
nearly collisionless plasma. Despite this, numerical simulations have so far
modeled these accretion flows using ideal magnetohydrodynamics. Here, we
present the first global, general relativistic, 3D simulations of accretion
flows onto a Kerr black hole including the non-ideal effects most likely to
affect the dynamics of the disk: the anisotropy between the pressure parallel
and perpendicular to the magnetic field, and the heat flux along magnetic field
lines. We show that for both standard and magnetically arrested disks, the
pressure anisotropy is comparable to the magnetic pressure, while the heat flux
remains dynamically unimportant. Despite this large pressure anisotropy,
however, the time-averaged structure of the accretion flow is strikingly
similar to that found in simulations treating the plasma as an ideal fluid. We
argue that these similarities are largely due to the interchangeability of the
viscous and magnetic shear stresses as long as the magnetic pressure is small
compared to the gas pressure, and to the sub-dominant role of pressure/viscous
effects in magnetically arrested disks. We conclude by highlighting outstanding
questions in modeling the dynamics of low collisionality accretion flows.
