  Mergers of binary neutron stars (NSs) usually result in the formation of a
hypermassive neutron star (HMNS). Whether- and when this remnant collapses to a
black hole (BH) depends primarily on the equation of state and on angular
momentum transport processes, both of which are uncertain. Here we show that
the lifetime of the merger remnant may be directly imprinted in the
radioactively powered kilonova emission following the merger. We employ
axisymmetric, time-dependent hydrodynamic simulations of remnant accretion
disks orbiting a HMNS of variable lifetime, and characterize the effect of this
delay to BH formation on the disk wind ejecta. When BH formation is relatively
prompt (~ 100 ms), outflows from the disk are sufficiently neutron rich to form
heavy r-process elements, resulting in ~ week-long emission with a spectral
peak in the near-infrared (NIR), similar to that produced by the dynamical
ejecta. In contrast, delayed BH formation allows neutrinos from the HMNS to
raise the electron fraction in the polar direction to values such that
potentially Lanthanide-free outflows are generated. The lower opacity would
produce a brighter, bluer, and shorter-lived ~ day-long emission (a `blue
bump') prior to the late NIR peak from the dynamical ejecta and equatorial
wind. This new diagnostic of BH formation should be useful for events with a
signal to noise lower than that required for direct detection of gravitational
waveform signatures.
