Asymptotic behaviour of cylindrical waves interacting with spinning strings

We consider a family of cylindrical spacetimes endowed with angular momentu m that are solutions to the vacuum Einstein equations outside the symmetry axis. This family was recently obtained by performing a complete gauge fixi ng adapted to cylindrical symmetry. In this paper, we find boundary conditi ons that ensure that the metric arising from this gauge fixing is well defi ned and that the resulting reduced system has a consistent Hamiltonian dyna mics. These boundary conditions must be imposed both on the symmetry axis a nd in the region far from the axis at spacelike infinity. Employing such co nditions, we determine the asymptotic behaviour of the metric close to and far from the axis. In each of these regions, the approximate metric describ es a conical geometry with a time dislocation. In particular, around the sy mmetry axis the effect of the singularity consists in inducing a constant d eficit angle and a timelike helical structure. Based on these results and o n the fact that the degrees of freedom in our family of metrics coincide wi th those of cylindrical vacuum gravity, we argue that the analysed set of s pacetimes represent cylindrical gravitational waves surrounding a spinning cosmic string. For any of these spacetimes, a prediction of our analysis is that the wave content increases the deficit angle at spatial infinity with respect to that detected around the axis.