  Mass accretion by black holes (BHs) is typically capped at the Eddington
rate, when radiation's push balances gravity's pull. However, even exponential
growth at the Eddington-limited e-folding time t_E ~ few x 0.01 billion years,
is too slow to grow stellar-mass BH seeds into the supermassive luminous
quasars that are observed when the universe is 1 billion years old. We propose
a dynamical mechanism that can trigger supra-exponential accretion in the early
universe, when a BH seed is trapped in a star cluster fed by the ubiquitous
dense cold gas flows. The high gas opacity traps the accretion radiation, while
the low-mass BH's random motions suppress the formation of a slowly-draining
accretion disk. Supra-exponential growth can thus explain the puzzling
emergence of supermassive BHs that power luminous quasars so soon after the Big
Bang.
