We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful stationary cylindrically symmmetric distributions of matter, smoothly matched to Lewis vacuum spacetime. A specific example is given. The electric and magnetic parts of the Weyl tensor are calculated, and it is shown that purely electric solutions are necessarily static. Then, it is shown that no conformally flat stationary cylindrical fluid exits, satisfying regularity and matching conditions. *

͑2͒ In Eq. ͑29͒ the expression for p z should take the formwhile the ones for and p remain the same. ͑3͒ Equation ͑30͒ should be written asshould be replaced by ͑33͒The rest of the paper, including the conclusions, remains the same.

The Wright and Lanczos solutions are studied, which represent the gravitational field produced by a rigidly rotating dust cylinder coupled with the cosmological constant. It is shown that when certain physical conditions are imposed the five-parameter Wright solutions reduce to the two-parameter Lanczos solutions. The geodesic motion of test particles in the Lanczos spacetime is then studied. The effects of the cosmological constant on the motion are investigated. It is found that confinement occurs quite generally in the radial direction, whereas the motion in the axial direction is free. The possible relevance of the confinement to extragalactic jet formation is pointed out.

Cylindrical spacetimes with rotation are studied using the Newmann-Penrose formulas. By studying null geodesic deviations the physical meaning of each component of the Riemann tensor is given. These spacetimes are further extended to include rotating dynamic shells, and the general expression of the surface energy-momentum tensor of the shells is given in terms of the discontinuation of the first derivatives of the metric coefficients. As an application of the developed formulas, a stationary shell that generates the Lewis solutions, which represent the most general vacuum cylindrical solutions of the Einstein field equations with rotation, is studied by assuming that the spacetime inside the shell is flat. It is shown that the shell can satisfy all the energy conditions by properly choosing the parameters appearing in the model, provided that $ 0 \le \sigma \le 1$, where $\sigma$ is related to the mass per unit length of the shell.Comment: Typed in Revtex, including three figures. To appear in General Relativity and Gravit