Exact impulsive gravitational waves in spacetimes of constant curvature

Exact solutions exist which describe impulsive gravitational waves propagating in Minkowski, de Sitter, or anti-de Sitter universes. These may be either nonexpanding or expanding. Both cases in each background are reviewed here from a unified point of view. All the main methods for their construction are described systematically: the Penrose "cut and paste" method, explicit construction of continuous coordinates, distributional limits of sandwich waves, embedding from higher dimensions, and boosts of sources or limits of infinite accelerations. Attention is concentrated on the most interesting specific solutions. In particular, the nonexpanding impulsive waves that are generated by null multipole particles are described. These generalize the well-known Aichelburg-Sexl and Hotta-Tanaka monopole solutions. Also described are the expanding spherical impulses that are generated by snapping and colliding strings. Geodesics and some other properties of impulsive wave spacetimes are also summarized.Comment: 33 pages, LaTeX 2e, in Gravitation: Following the Prague Inspiration (To celebrate the 60th birthday of Jiri Bicak), O.Semerak, J.Podolsky, M.Zofka (eds.), World Scientific, Singapore, to appear in 2002, pp 205-24

Chaos in Kundt type III Spacetimes

We consider geodesics motion in a particular Kundt type III spacetime in which Einstein-Yang-Mills equations admit solutions. On a particular surface as constraint we project the geodesics into the (x,y) plane and treat the problem as a 2-dimensional one. Our numerical study shows that chaotic behavior emerges under reasonable conditions.Comment: 4 Figure

Chaotic motion in pp-wave spacetimes

We investigate geodesics in non-homogeneous vacuum pp-wave solutions and demonstrate their chaotic behavior by rigorous analytic and numerical methods. For the particular class of solutions considered, distinct "outcomes" (channels to infinity) are identified, and it is shown that the boundary between different outcomes has a fractal structure. This seems to be the first example of chaos in exact radiative spacetimes.Comment: 15 pages (latex),12 figures (gif), to appear in Class. Quantum Gra