  As part of our effort to search for circumstellar disks around high-mass
stellar objects, we observed the well-known core G31.41+0.31 with ALMA at 1.4
mm with an angular resolution of~0.22" (~1700 au). The dust continuum emission
has been resolved into two cores namely Main and NE. The Main core, which has
the stronger emission and is the more chemically rich, has a diameter of ~5300
au, and is associated with two free-free continuum sources. The Main core looks
featureless and homogeneous in dust continuum emission and does not present any
hint of fragmentation. Each transition of CH3CN and CH3OCHO, both ground and
vibrationally excited, as well as those of CH3CN isotopologues, shows a clear
velocity gradient along the NE-SW direction, with velocity linearly increasing
with distance from the center, consistent with solid-body rotation. However,
when comparing the velocity field of transitions with different upper level
energies, the rotation velocity increases with increasing energy of the
transition, which suggests that the rotation speeds up towards the center.
Spectral lines towards the dust continuum peak show an inverse P-Cygni profile
that supports the existence of infall in the core. The infall velocity
increases with the energy of the transition suggesting that the infall is
accelerating towards the center of the core, consistent with gravitational
collapse. Despite the monolithic appearance of the Main core, the presence of
red-shifted absorption, the existence of two embedded free-free sources at the
center, and the rotational spin-up are consistent with an unstable core
undergoing fragmentation with infall and differential rotation due to
conservation of angular momentum. Therefore, the most likely explanation for
the monolithic morphology is that the large opacity of the dust emission
prevents the detection of any inhomogeneity in the core.
