  Direct collapse of supermassive stars is a possible pathway to form
supermassive black hole seeds at high redshifts. Whereas previous
three-dimensional (3D) simulations demonstrate that supermassive stars form via
rapid mass accretion, those resolving the stellar interior have been limited.
We here report 3D radiation-hydrodynamic (RHD) simulations following the
evolution of rapidly accreting protostars resolving the stellar interior. We
use an adaptive mesh refinement code with our newly developed RHD solver
employing an explicit M1 closure method. We follow the early evolution until
the stellar mass reaches $\sim 10~M_\odot$ from two different initial
configurations of spherical and turbulent clouds. We demonstrate that, in both
the cases, a swollen protostar whose radius is $100\mathrm{-}1000~R_\odot$
appears, as predicted by the stellar evolution calculations. Its effective
temperature remains a few thousand Kelvin, and the radiative feedback by
ionizing photons is too weak to disturb the accretion flow up to the epoch
examined in this work. In the turbulent case, the protostar rotates rapidly at
more than 0.4 times the Keplerian velocity owing to the angular momentum
provided by the initial turbulence. The protostar approximates an oblate
spheroid, and its equatorial radius is more than twice the polar radius. Our
results suggest that we need to consider the rapid stellar rotation to
elucidate the realistic 3D protostellar evolution in the supermassive star
formation.
