  General relativity predicts that black hole images ought to display a bright,
thin (and as-of-yet-unresolved) ring. This "photon ring" is produced by photons
that explore the strong gravity of the black hole, flowing along trajectories
that experience extreme light bending within a few Schwarzschild radii of the
horizon before escaping. The shape of the photon ring is largely insensitive to
the precise details of the emission from the astronomical source surrounding
the black hole and therefore provides a direct probe of the Kerr geometry and
its parameters. The Black Hole Explorer (BHEX) is a proposed space-based
experiment targeting the supermassive black holes M87* and Sgr A* with
radio-interferometric observations at frequencies of 100 GHz through 300 GHz
and from an orbital distance of ~30,000 km. This design will enable
measurements of the photon rings around both M87* and Sgr A*, confirming the
Kerr nature of these sources and delivering sharp estimates of their masses and
spins.
