Primordial Black Hole Evaporation and Dark Matter Production: I. Solely
  Hawking radiation
  Hawking evaporation of black holes in the early Universe is expected to
copiously produce all kinds of particles, regardless of their charges under the
Standard Model gauge group. For this reason, any fundamental particle, known or
otherwise, could be produced during the black hole lifetime. This certainly
includes dark matter (DM) particles. This paper improves upon previous
calculations of DM production from primordial black holes (PBH) by consistently
including the greybody factors, and by meticulously tracking a system of
coupled Boltzmann equations. We show that the initial PBH densities required to
produce the observed relic abundance depend strongly on the DM spin, varying in
about $\sim 2$ orders of magnitude between a spin-2 and a scalar DM in the case
of non-rotating PBHs. For Kerr PBHs, we have found that the expected
enhancement in the production of bosons reduces the initial fraction needed to
explain the measurements. We further consider indirect production of DM by
assuming the existence of additional and unstable degrees of freedom emitted by
the evaporation, which later decay into the DM. For a minimal setup where there
is only one heavy particle, we find that the final relic abundance can be
increased by at most a factor of $\sim 4$ for a scalar heavy state and a
Schwarzschild PBH, or by a factor of $\sim 4.3$ for a spin-2 particle in the
case of a Kerr PBH.
