  We investigate general relativistic magnetohydrodynamic simulations (GRMHD)
to determine the physical origin of the twisty patterns of linear polarization
seen in spatially resolved black hole images and explain their morphological
dependence on black hole spin. By characterising the observed emission with a
simple analytic ring model, we find that the twisty morphology is determined by
the magnetic field structure in the emitting region. Moreover, the dependence
of this twisty pattern on spin can be attributed to changes in the magnetic
field geometry that occur due to the frame dragging. By studying an analytic
ring model, we find that the roles of Doppler boosting and lensing are
subdominant. Faraday rotation may cause a systematic shift in the linear
polarization pattern, but we find that its impact is subdominant for models
with strong magnetic fields and modest ion-to-electron temperature ratios.
Models with weaker magnetic fields are much more strongly affected by Faraday
rotation and have more complicated emission geometries than can be captured by
a ring model. However, these models are currently disfavoured by the recent EHT
observations of M87*. Our results suggest that linear polarization maps can
provide a probe of the underlying magnetic field structure around a black hole,
which may then be usable to indirectly infer black hole spins. The generality
of these results should be tested with alternative codes, initial conditions,
and plasma physics prescriptions.
