Thin cylindrical shell of dust under rigid rotation in general relativity

Abstract

Following the method developed by Papapetrou and Hamoui, a solution of the Einstein equations corresponding to a thin shell of dust under rigid rotation solution is obtained. The region interior to the shell is flat and the exterior vacuum region is chosen as a Lewis manifold. An essential limitation of this type of shell is that it does not allow the limitM ₁ andL ₁→ 0, whereM ₁ andL ₁ are the mass and the angular momentum per unit length. It is shown that the limitation is a consequence of the fact that the Lewis metric does not contain the Minkowski metric as a special case.