Asymptotic behaviour of cylindrical waves interacting withspinning strings

Abstract

We consider a family of cylindrical spacetimesendowed with angular momentum that aresolutions to the vacuum Einstein equationsoutside the symmetry axis. This family wasrecently obtained by performing a completegauge fixing adapted to cylindrical symmetry.In this paper, we find boundary conditionsthat ensure that the metric arising from thisgauge fixing is well defined and that theresulting reduced system has a consistentHamiltonian dynamics. These boundaryconditions must be imposed both on thesymmetry axis and in the region far from theaxis at spacelike infinity. Employing suchconditions, we determine the asymptoticbehaviour of the metric close to and far fromthe axis. In each of these regions, theapproximate metric describes a conicalgeometry with a time dislocation. Inparticular, around the symmetry axis theeffect of the singularity consists in inducinga constant deficit angle and a timelikehelical structure. Based on these results andon the fact that the degrees of freedom inour family of metrics coincide with those ofcylindrical vacuum gravity, we argue that theanalysed set of spacetimes representcylindrical gravitational waves surrounding aspinning cosmic string. For any of thesespacetimes, a prediction of our analysis isthat the wave content increases the deficitangle at spatial infinity with respect tothat detected around theaxis.