  Classical black holes contain a singularity at their core. This has prompted
various researchers to propose a multitude of modified spacetimes that mimic
the physically observable characteristics of classical black holes as best as
possible, but that crucially do not contain singularities at their cores. Due
to recent advances in near-horizon astronomy, the ability to observationally
distinguish between a classical black hole and a potential black hole mimicker
is becoming increasingly feasible. Herein, we calculate some physically
observable quantities for a recently proposed regular black hole with an
asymptotically Minkowski core -- the radius of the photon sphere and the
extremal stable timelike circular orbit (ESCO). The manner in which the photon
sphere and ESCO relate to the presence (or absence) of horizons is much more
complex than for the Schwarzschild black hole. We find situations in which
photon spheres can approach arbitrarily close to (near extremal) horizons,
situations in which some photon spheres become stable, and situations in which
the locations of both photon spheres and ESCOs become multi-valued, with both
ISCOs (innermost stable circular orbits) and OSCOs (outermost stable circular
orbits). This provides an extremely rich phenomenology of potential
astrophysical interest.
