The gravitational fields of some rotating and nonrotating cylindrical shells of matter, John Statchel, J. Math. Phys. 25(2) (1984)
The exterior and flat interior metrics of an infinite cylindrical shell (surface layer) of matter are studied, for nonrotating and rigidly rotating shells. Relations between the parameters characterizing the exterior metric and the components of the shell's stress-energy tensor are established. It is shown that one of these parameters, characterizing the "conicality" of the exterior field, is related to the energy density of the source; while another, characterizing local nonflatness, is related to certain components of the stress-tensor. A one-parameter family of locally flat but conical exterior metrics generated by a particular type of massive cylindrical shells is exhibited. The globally stationary but locally static exterior field of a rigidly rotating shell is studied. The (nonlocal) parameter of the exterior field characterizing the rotation is related to the rate of rotation of the of the shell as defined by the flat interior metric.