  We investigate the spontaneous creation of primordial black holes in a
lower-dimensional expanding early universe. We use the no-boundary proposal to
construct instanton solutions for both the background and a black hole
nucleated inside this background. The resulting creation rate could lead to a
significant population of primordial black holes during the lower dimensional
phase. We also consider the subsequent evaporation of these dimensionally
reduced black holes and find that their temperature increases with mass,
whereas it decreases with mass for 4-dimensional black holes. This means that
they could leave stable sub-Planckian relics, which might in principle provide
the dark matter.
