  In order to avoid unphysical causality-violating effects any rigidly rotating
system must be bounded in directions transverse to the axis of rotation. We
demonstrate that this requirement implies substantial dependence of properties
of relativistically rotating system on the boundary conditions. We consider a
system of interacting fermions described by the Nambu-Jona-Lasinio model in a
space bounded by cylindrical surface of finite radius. In order to confine the
fermions inside the cylinder we impose "chiral" MIT boundary conditions on its
surface. These boundary conditions are parameterized by a continuous chiral
angle \Theta. We find that at any value of \Theta the chiral restoration
temperature T_c decreases as a quadratic function of the angular frequency
\Omega. However, the position and the slope of the critical curve T_c =
T_c(\Omega) in the phase diagram depends noticeably on the value of the chiral
angle.
