  Radiative feedback from massive Population III (Pop III) stars in the form of
ionising and photodissociating photons is widely believed to play a central
role in shutting off accretion onto these stars. Understanding whether and how
this occurs is vital for predicting the final masses reached by these stars and
the form of the Pop III stellar initial mass function. To help us better
understand the impact of UV radiation from massive Pop III stars on the gas
surrounding them, we carry out high resolution simulations of the formation and
early evolution of these stars, using the AREPO moving-mesh code coupled with
the innovative radiative transfer module SPRAI. Contrary to most previous
results, we find that the ionising radiation from these stars is trapped in the
dense accretion disk surrounding them. Consequently, the inclusion of radiative
feedback has no significant impact on either the number or the total mass of
protostars formed during the 20 kyr period that we simulate. We show that the
reason that we obtain qualitatively different results from previous studies of
Pop III stellar feedback lies in how the radiation is injected into the
simulation. HII region trapping only occurs if the photons are injected on
scales smaller than the local scale height of the accretion disk, a criterion
not fulfilled in previous 3D simulations of this process. Finally, we speculate
as to whether outflows driven by the magnetic field or by Lyman-alpha radiation
pressure may be able to clear enough gas away from the star to allow the HII
region to escape from the disk.
