  The spectacular images of the M87 black hole taken by the Event Horizon
Telescope (EHT) have opened a new era of black hole research. One of the next
issues is to take polarization images around the central black hole (BH). Since
radio emission is produced by synchrotron process, polarization properties
should vividly reflect the magnetic field structure at the jet base and thus
provide good information regarding the magnetic mechanism of jet formation.
With this kept in mind we perform general relativistic (GR) radiative transfer
calculations of polarized light based on the GR magnetohydrodynamic (MHD)
simulation data of accretion flow and outflow in M87, to obtain their linear
and circular polarization images in the horizon-scale. We found that the linear
polarization components from the jet base and inner accretion flow should
experience Faraday rotation when passing through magnetized plasmas around the
BH, thus sensitively depending on the BH spin. Through the comparison with
intensity image at 1.3mm by EHT and the polarized degree and the rotation
measure (RM) at 1.3mm with the Submillimeter Array, the model with the spin
parameter of a=0.9M_BH (with M_BH being the BH mass) is favored over other
models with a=0.5M_BH or 0.99M_BH, though we need further systematic studies
for confirmation. We also find in low-temperature models clear ring-like image
in the circular polarization map, which arises because of Faraday conversion of
the linearly polarized synchrotron emission and is thus indicative of magnetic
field. This occurs only when the emission region is threaded with well-ordered
magnetic fields and hence no clear images are expected in high-temperature disk
models, in which disk emission is appreciable. We will be able to elucidate the
field configuration through the comparison between the simulated polarization
images and future polarimetry with EHT and other VLBI observations.
