We present a new family of exact solutions of the Einstein-Maxwell equations for cylindrically symmetric nonstationary space-times. The solutions can be interpreted as describing the presence of a rotating cosmic string interacting with electromagnetic and gravitational radiation. We show, by appropriate identifications, that our solutions include as subfamilies, and generalize, all the known results on this type of space-times recently obtained by Xanthopoulos and by Economou and Tsoubelis. We include also an analysis of the general structure of the solutions, the Maxwell and Weyl scalars and their asymptotic behavior. The solitonic behavior of the waves is depicted both in the form of a perturbation of the metric coefficients and as a nonvanishing flux of C energy at null infinity. We also show that our solutions contain a subfamily with hypersurface-orthogonal Killing vectors. The metrics were obtained using Alekseev's inverse scattering method. Their relation with those obtained with other methods is briefly considered. I. I N T R O D U C T I O NT h e mechanism of galaxy formation t h a t attributes t h e initial perturbations t o t h e presence and evolution of cosmic strings, created as the result of the symmetry breaking predicted by grand unified theories, has been t h e subject of a n important research effort. A good review of cosmic strings can b e found in t h e article by Vilenkin.' Most of the work on this subject, however, has been carried o u t under t h e assumption t h a t general relativistic-effects outside t h e string can be disregarded. Exact solutions t h a t include t h e full general-relativistic effects are therefore of interest, as they can give a better understanding of t h e approximations involved, as well a s mark t h e possibility of new processes not considered previously.2 Some results o n exact solutions with closed strings are known.3 However, because of t h e simplification t h a t results from their higher symmetry, most of the research work has been concentrated on open isolated infinitely long strings, as they correspond t o systems having cylindrical symmetry.In general, t h e requirements for a n exact solution t o represent a n isolated cosmic string are t h a t they should have a regular symmetry axis a n d t h a t they should b e asymptotically flat far away from t h e axis. One may also require t h a t t h e solution be smooth and singularity-free everywhere, except, of course, for t h e characteristic conical singularity on the axis. T h e condition of regularity on t h e symmetry axis probably does not hold if we are dealing with superconducting strings, because it is expected t h a t t h e presence of a current should lead t o some singularity on t h a t axis.4 Some solutions recently found t h a t describe a superconducting cosmic string, have precisely t h a t kind of b e h a~i o r .~ In t h e nonsuperconducting case, several exact solutions (all of Petrov type D), representing a n infinite straight cosmic strings surrounded by, a n d possibly interacting with, ...

We present several noiltrivial limits of a new family of exact solutions of the Einstcin-Maxwell equations for axisymmetric ilonstationary spacetimes, obtained using Alekseev's inverse-scattering method, which we previously interpreted as describing the presence of a rotating cosinic string iilteracting with electromagnetic and gravitational radiation. The liinit in which the C energy of the solutions goes to infinity is related to a change in their geometry, reminiscer~t of some results recently found for both gauge and global cos~~lic strings. T l~e axisymmetry, i.e., the presence of a (quasiregular) symmetry "axis," is in general lost,, except in one case, which i~lcludes h~~persurface-ortl~ogoilal Killing vectors. Its relation to Xantl~oponlos's question as to ~vhcthcr the "rotation" can be stopped is discussed. 'This last casc can also be interpreted as a collapsiilg Melvin electroinagiletic universe. We also analyze a partic~~lar limit that leads to a vacuum solutio~l with a curvature singularity on the sylnmetry axis, 11111 asy~nptotically flat in t l~e radial direction.

The authors analyse the asymptotic behaviour at past and future null infinity of several scalars and observable quantities in vacuum Einstein-Rosen solitary-like waves. They construct an explicit example and, in all cases, they find a time shift of the corresponding amplitudes as compared with, for example, the propagation of massless 'test' particles. The magnitude of the shift depends on the quantity considered but in all cases it increases monotonically with the C-energy or, equivalently, the deficit angle at infinity, growing indefinitely as the deficit angle approaches 2 pi .

The authors present a family of solutions of the Einstein-Maxwell equations obtained as a two-soliton transformation of a Minkowskian seed, using Alekseev's inverse scattering method (AISM). For general values of the arbitrary parameters that arise from the AISM, the metrics are of Petrov type I, and represent cylindrically symmetric perturbations of a conical spacetime ('thin cosmic string'), that preserve the asymptotic flatness of the background, up to an additional deficit angle. The metrics can be made regular on the symmetry axis by an adequate choice of parameters. In the limit in which the C-energy goes to infinity, the metric is singular, but can be 'renormalized', obtaining either (i) a family of metrics where the symmetry axis contains a curvature singularity, or (ii) a family of cylindrically symmetric metrics with a regular axis, that can be interpreted as simple solitonic perturbations of an unstable Melvin universe. These contain a subfamily of diagonal metrics. They include a comparison with other metrics, obtained as limiting cases and, in the case of vacuum solutions, they show, by an explicit calculation, that the results obtained are equivalent to the Belinski-Zakharov transformation for two pairs of complex-conjugate soliton poles for the same seed.

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