An exterior solution of the einstein field equations for a rotating infinite cylinder

We give here a new exact solution to the exterior Einstein field equations for a rotating infinite cylinder. The solution is characterized by an everywhere singular metric. In the Papapetrou canonical coordinates, the 3-force acting on a radially moving test particle is $f^\alpha = \left( {G\frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{\lambda }{\rho },{\text{ 0,}} - \frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{{C\upsilon }}{\rho }{\text{ }}} \right)$ where λ>0.f ¹ andf ³ are, respectively, the gravitational and Coriolis forces. The gravitational force is, therefore, repulsive.