The role of stellar relaxation in the formation and evolution of the
  first massive black holes
  We present calculations on the formation of massive black holes with 10^5
Msun at z > 6 that can be the seeds of supermassive black holes at z > 6. Under
the assumption of compact star cluster formation in merging galaxies, star
clusters in haloes of 10^8 ~ 10^9 Msun can undergo rapid core-collapse leading
to the formation of very massive stars (VMSs) with ~1000 Msun which directly
collapse into black holes with similar masses. Star clusters in halos of > 10^9
Msun experience type-II supernovae before the formation of VMSs due to long
core-collapse time scales. We also model the subsequent growth of black holes
via accretion of residual stars in clusters. 2-body relaxation efficiently
re-fills the loss cones of stellar orbits at larger radii and resonant
relaxation at small radii is the main driver for accretion of stars onto black
holes. As a result, more than ninety percent of stars in the initial cluster
are swallowed by the central black holes before z=6. Using dark matter merger
trees we derive black hole mass functions at z=6-20. The mass function ranges
from 10^3 to 10^5 Msun at z <~ 15. Major merging of galaxies of >~ 4*10^8 Msun
at z ~ 20 successfully leads to the formation of >~ 10^5 Msun BHs by z >~ 10
which can be the potential seeds of supermassive black holes seen today.
