  We report on a calculation of the growth of the mass of supermassive black
holes at galactic centers from dark matter and Eddington - limited baryonic
accretion. Assuming that dark matter halos are made of fermions and harbor
compact degenerate Fermi balls of masses from $10^{3}M_{\odot}$ to
$10^{6}M_{\odot}$, we find that dark matter accretion can boost the mass of
seed black holes from about $\sim 5M_{\odot}$ to $10^{3-4}M_{\odot}$ black
holes, which then grow by Eddington - limited baryonic accretion to
supermassive black holes of $10^{6 - 9}M_{\odot}$. We then show that the
formation of the recently detected supermassive black hole of $3\times
10^{9}M_{\odot}$ at a redshift of $z = 6.41$ in the quasar SDSS
J114816.64+525150.3 could be understood if the black hole completely consumes
the degenerate Fermi ball and then grows by Eddington - limited baryonic
accretion. In the context of this model we constrain the dark matter particle
masses to be within the range from 12 ${\rm keV/c}^{2}$ to about 450 ${\rm
keV/c}^{2}$. Finally we investigate the black hole growth dependence on the
formation time of the seed BH and on the mass of the seed BH. We find that in
order to fit the observed data point of $M_{BH} \sim 3 \times 10^{9}M_{\odot}$
and $z \sim 6.41$, dark matter accretion cannot start later than about $2
\times 10^{8}$ years and the seed BH cannot be greater than about
$10^{4}M_{\odot}$. Our results are in full agreement with the WMAP observations
that indicate that the first onset of star formation might have occurred at a
redshift of $z \sim 15 - 20$. For other models of dark matter particle masses,
corresponding constraints may be derived from the growth of black holes in the
center of galaxies.
