Primordial black holes in a dimensionally reduced universe

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 signi fi cant population of primordial black holes during the lower dimensional phase. We also consider the subsequent evaporation of these dimensionally reduced black holes and fi nd 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.