  Stability properties of gravitationally bound condensates composed of
ultralight axionic Fuzzy Dark Matter (FDM) are studied. Previous work has shown
that astrophysical collisions could make self-gravitating condensates
structurally unstable, making them prone to collapse and decay; in the context
of FDM, we reexamine the relevant timescales using the time-dependent
variational method. We show that FDM condensates can be made unstable through
gravitational interactions with central black holes, for black hole masses in a
phenomenologically relevant range. Instability could also be stimulated by
galaxy collisions. The subsequent decay takes place over a period lasting as
long as many thousands of years. We also discuss the possible relevance of FDM
condensates to understanding the composition of Ultracompact Dwarf (UCD)
Galaxies. Future observation of extremely massive black holes in the central
regions of UCDs can constrain this interpretation.
