Dynamics of rotating cylindrical shells in general relativity

Cylindrical spacetimes with rotation are studied using the Newmann-Penrose formulas. By studying null geodesic deviations, the physical meaning of eac h component of the Riemann tensor is given. These spacetimes are further ex tended to include rotating dynamic shells, and the general expression of th e surface energy-momentum tensor of the shells is given in terms of the dis continuity of the first derivatives of the metric coefficients. As an appli cation of the developed formulas, a stationary shell that generates the Lew is 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 sat isfy all the energy conditions by properly choosing the parameters appearin g in the model, provided that 0 less than or equal to sigma less than or eq ual to 1, where sigma is related to the mass per unit length of the shell.