Relativistic superfluidity and vorticity from the nonlinear Klein-Gordon equation

We investigate superfluidity, and the mechanism for creation of quantized vortices, in the relativistic regime. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics gives rise to superfluidity. The mechanisms discussed are local inertial forces (Coriolis and centrifugal), and current-current interaction with an external source. The primary application is to cosmology, but we also discuss the reduction to the non-relativistic nonlinear Schr\"{o}dinger equation, which is widely used in describing superfluidity and vorticity in liquid helium and cold-trapped atomic gases.