Axisymmetric electrovacuum spacetimes with a translational Killing vector at null infinity

By using the Bondi-Sachs-van der Burg formalism we analyze the asymptotic properties at null infinity of axisymmetric electrovacuum spacetimes with a translational Killing vector and, in general, an infinite ``cosmic string'' (represented by a conical singularity) along the axis. Such spacetimes admit only a local null infinity. There is a non-vanishing news function due to the existence of the string even though there is no radiation. We prove that if null infinity has a smooth compact cross section and the spacetime is not flat in a neighbourhood of null infinity, then the translational Killing vector must be timelike and the spacetime is stationary. The other case in which an additional symmetry of axisymmetric spacetimes admits compact cross sections of null infinity is the boost symmetry, which leads to radiative spacetimes representing ``uniformly accelerated objects''. These cases were analyzed in detail in our previous works. If the translational Killing vector is spacelike or null, corresponding to cylindrical or plane waves, some complete generators of null infinity are ``singular'' but null infinity itself can be smooth apart from these generators. As two explicit examples of local null infinity, Schwarzschild spacetime with a string and a class of cylindrical waves with a string are discussed in detail in the Appendix.Comment: 15 pages, RevTeX, submitted to Class. Quantum Gra

Expanding impulsive gravitational waves

We explicitly demonstrate that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a "cut and paste" method may be considered to be impulsive limits of the Robinson-Trautman vacuum type N solutions. We extend these results to all the generically distinct subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter backgrounds. For these we express the solutions in terms of a continuous metric. Finally, we also extend the class of spherical shock gravitational waves to include a non-zero cosmological constant.Comment: 11 pages, LaTeX, To appear in Class. Quantum Gra

Behavior of Einstein-Rosen Waves at Null Infinity

The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof. Somewhat surprisingly, the behavior in a generic direction is {\it better} than that in directions orthogonal to the symmetry axis. The geometric origin of this difference can be understood most clearly from the 3-dimensional perspective.Comment: 16 pages, REVETEX, CGPG-96/5-

Global structure of Robinson-Trautman radiative space-times with cosmological constant

Robinson-Trautman radiative space-times of Petrov type II with a non-vanishing cosmological constant Lambda and mass parameter m>0 are studied using analytical methods. They are shown to approach the corresponding spherically symmetric Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter solution at large retarded times. Their global structure is analyzed, and it is demonstrated that the smoothness of the extension of the metrics across the horizon, as compared with the case Lambda=0, is increased for Lambda>0 and decreased for Lambda0 exhibit explicitly the cosmic no-hair conjecture under the presence of gravitational waves

Co-accelerated particles in the C-metric

With appropriately chosen parameters, the C-metric represents two uniformly accelerated black holes moving in the opposite directions on the axis of the axial symmetry (the z-axis). The acceleration is caused by nodal singularities located on the z-axis. In the~present paper, geodesics in the~C-metric are examined. In general there exist three types of timelike or null geodesics in the C-metric: geodesics describing particles 1) falling under the black hole horizon; 2)crossing the acceleration horizon; and 3) orbiting around the z-axis and co-accelerating with the black holes. Using an effective potential, it can be shown that there exist stable timelike geodesics of the third type if the product of the parameters of the C-metric, mA, is smaller than a certain critical value. Null geodesics of the third type are always unstable. Special timelike and null geodesics of the third type are also found in an analytical form.Comment: 10 pages, 12 EPS figures, changes mainly in abstract & introductio

The collision and snapping of cosmic strings generating spherical impulsive gravitational waves

The Penrose method for constructing spherical impulsive gravitational waves is investigated in detail, including alternative spatial sections and an arbitrary cosmological constant. The resulting waves include those that are generated by a snapping cosmic string. The method is used to construct an explicit exact solution of Einstein's equations describing the collision of two nonaligned cosmic strings in a Minkowski background which snap at their point of collision.Comment: 10 pages, 6 figures, To appear in Class. Quantum Gra