A. Garcia et D. Kramer, STATIONARY CYLINDRICALLY SYMMETRICAL GRAVITATIONAL-FIELDS WITH DIFFERENTIALLY ROTATING PERFECT FLUIDS, Classical and quantum gravity, 14(2), 1997, pp. 499-508
A wide family of stationary cylindrically symmetric gravitational fiel
ds with differentially rotating perfect fluids as a source are derived
. Among them there are solutions given in terms of trigonometric, hype
rbolic and Whittaker functions. A class of stationary cylindrically sy
mmetric solutions with a rigidly rotating perfect fluid is derived. Th
e reported metrics belong to the algebraically general Petrov type.