  The Event Horizon Telescope (EHT) Collaboration has recently published the
first horizon-scale images of the supermassive black holes M87* and Sgr A* and
provided some first information on the physical conditions in their vicinity.
The comparison between the observations and the three-dimensional
general-relativistic magnetohydrodynamic (GRMHD) simulations has enabled the
EHT to set initial constraints on the properties of these black-hole
spacetimes. However, accurately distinguishing the properties of the accretion
flow from those of the spacetime, most notably, the black-hole mass and spin,
remains challenging because of the degeneracies the emitted radiation suffers
when varying the properties of the plasma and those of the spacetime. The
next-generation EHT (ngEHT) observations are expected to remove some of these
degeneracies by exploring the complex interplay between the disk-jet dynamics,
which represents one of the most promising tools for extracting information on
the black-hole spin. By using GRMHD simulations of magnetically arrested disks
(MADs) and general-relativistic radiative-transfer (GRRT) calculations of the
emitted radiation, we have studied the properties of the jet and the
accretion-disk dynamics on spatial scales that are comparable with the horizon.
In this way, we are able to highlight that the radial and azimuthal dynamics of
the jet are well correlated with the black-hole spin. Based on the resolution
and image reconstruction capabilities of the ngEHT observations of M87*, we can
assess the detectability and associated uncertainty of this correlation.
Overall, our results serve to assess what are the prospects for constraining
the black-hole spin with future EHT observations.
