  The origin of our universe's cosmological magnetic fields remains a mystery.
In this study, we consider whether these magnetic fields could have been
generated in the early universe by a population of charged, spinning primordial
black holes. To this end, we calculate the strength and correlation length of
the magnetic fields generated by this population, and describe their evolution
up to the current epoch. We find that near-extremal black holes in the mass
range $ M \sim 10^{28} -10^{36} \, {\rm g}$ could potentially generate magnetic
fields with present day values as large as $B \sim 10^{-20} - 10^{-15} \, {\rm
G}$; those with $M \gtrsim10^{38} \, \rm{g}$ could have produced even larger
fields $B \gtrsim 10^{-14} \, {\rm G}$. To motivate this scenario, we briefly
discuss how new physics may have induced a chemical potential which could have
briefly maintained the black holes in an electrically charged state in the
early universe. Finally, we comment on a correlation between the parameters of
the cosmological magnetic field and the stochastic gravitational wave
background coming from the merger of primordial black hole binaries as the
primary observable signature of this scenario.
