Constraining the mass density of free-floating black holes using
  razor-thin lensing arcs
  Strong lensing of active galactic nuclei in the radio can result in
razor-thin arcs, with a thickness of less than a milli-arcsecond, if observed
at the resolution achievable with very long baseline interferometry (VLBI).
Such razor-thin arcs provide a unique window on the coarseness of the matter
distribution between source and observer. In this paper, we investigate to what
extent such razor-thin arcs can constrain the number density and mass function
of `free-floating' black holes, defined as black holes that do not, or no
longer, reside at the centre of a galaxy. These can be either primordial in
origin or arise as by-products of the evolution of super-massive black holes in
galactic nuclei. When sufficiently close to the line of sight, free-floating
black holes cause kink-like distortions in the arcs, which are detectable by
eye in the VLBI images as long as the black hole mass exceeds $\sim 1000$ Solar
masses. Using a crude estimate for the detectability of such distortions, we
analytically compute constraints on the matter density of free-floating black
holes resulting from null-detections of distortions along a realistic, fiducial
arc, and find them to be comparable to those from quasar milli-lensing. We also
use predictions from a large hydrodynamical simulation for the demographics of
free-floating black holes that are not primordial in origin, and show that
their predicted mass density is roughly four orders of magnitude below the
constraints achievable with a single razor-thin arc.
