The double-dust solution

An exact solution describing the static gravitational field produced by the superposition of two dust beams of equal mass density but opposite propagation direction is given in a closed form. In particular, the cylindrically symmetric situation is considered in which the two dust components move on trajectories screwing around the axis. In this case, the solution can be matched to the Levi-Civita external vacuum solution at any value of the radial coordinate. The axis is regular and the mass density is positive everywhere in the interior region of the global solution. The dominant energy condition is satisfied