  Using first-principle numerical simulations, we find a new spatially
inhomogeneous phase in rigidly rotating $N_c = 3$ gluon plasma. This mixed
phase simultaneously possesses both confining and deconfining phases in thermal
equilibrium. Unexpectedly, the local critical temperature of the phase
transition at the rotation axis does not depend on the angular frequency within
a few percent accuracy. Even more surprisingly, an analytic continuation of our
results to the domain of real angular frequencies indicates a profound breaking
of the Tolman-Ehrenfest law in the vicinity of the phase transition, with the
confining (deconfining) phase appearing far (near) the rotation axis.
