Firewall boundaries and mixed phases of rotating quark matter in linear sigma model

A rigidly-rotating body in unbounded space is usually considered a pathological system since it leads to faster-than-light velocities and associated breaches of causality. However, numerical results on chiral symmetry breaking in rotating plasmas of interacting fermions reveal surprisingly close correspondence in predictions between the rigorous bounded and formal unbounded approaches. To provide insight into this correlation, we consider the linear sigma model coupled to quarks, undergoing rigid rotation in unbounded Minkowski space-time. Within the mean-field approach, we adopt three consecutive levels of approximation to the ground state of the system that feature uniform (model 1), weakly inhomogeneous (model 2) and fully inhomogeneous (model 3) condensates. Models 1 and 2 that do not take into account spatial gradients of the condensate show agreement with the Tolman-Ehrenfest law. Model 3 exhibits a deviation from the Tolman-Ehrenfest prediction due to the appearance of a new energy scale set by the inhomogeneity of the ground state. Its boundary conditions are fixed by imposing regularity at the rotation axis and by demanding the global minimization of the grand potential. We dub the latter as ``firewall boundary conditions,'' translating into the requirement of vanishing condensate on the light cylinder, which follows from the fact that the system state formally diverges at the light cylinder. In all models, we present the phase diagram of the system and point out that in models 2 and 3, the system resides either in a chirally-restored phase, or in a mixed phase that possesses spatially-separated chirally-restored and chirally-broken phases. Finally, we discuss the properties of the system under inhomogeneous rotation using the relativistic version of the Rankine vortex model.