Stationary perfect fluid cylinders

Abstract

Using the formalism of Kramer for the stationary, cylindrically symmetric and rigidly rotating perfect fluid, two models are derived explicitly. The solutions are regular on the axis and the energy conditions are satisfied for a certain range of the angular velocity. In the limit of no rotation they are reduced to the Kramer (p = (-1)µ) and Evans (µ = 5p+constant) static cylindrically symmetric metrics.