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

New mixed inhomogeneous phase in vortical gluon plasma: first-principle results from rotating SU(3) lattice gauge theory