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.
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