Seed black holes formed in the collapse of population III stars have been invoked to explain the presence of supermassive black holes at high redshift .
It has been suggested that a seed black hole can grow up to 10 ^ { 5 \sim 6 } M _ { \odot } through highly super-Eddington accretion for a period of \sim 10 ^ { 6 \sim 7 } yr between redshift z = 20 \sim 24 .
We studied the feedback of radiation pressure , Compton heating and outflow during the seed black hole growth .
It is found that its surrounding medium fueled to the seed hole is greatly heated by Compton heating .
For a super-critical accretion onto a 10 ^ { 3 } M _ { \odot } seed hole , a Compton sphere ( with a temperature \sim 10 ^ { 6 } K ) forms in a timescale of 1.6 \times 10 ^ { 3 } yr so that the hole is only supplied by a rate of 10 ^ { -3 } Eddington limit from the Compton sphere .
Beyond the Compton sphere , the kinetic feedback of the strong outflow heats the medium at large distance , this leads to a dramatical decrease of the outer Bondi accretion onto the black hole and avoid the accumulation of the matter .
The highly super-critical accretion will be rapidly halted by the strong feedback .
The seed black holes hardly grow up at the very early universe unless the strong feedback can be avoided .