Colliding gravitational waves and singularities

We have investigated a model of colliding plain gravitational waves, proposed by Szekeres, whose structure of singularities is determined. We have evaluated a total energy of matter as a volume integral of the energy-momentum tensor (EMT), whose contributions arise only at these singularities. The total matter energy is conserved before a collision of two plane gravitational waves but decreases during the collision and becomes zero at the end of the collision. We thus interpret that this model of colliding plane gravitational waves is a space-time describing a pair annihilation of plan gravitational waves. We have also calculated a matter conserved charge proposed by the present author and his collaborators. The matter charge is indeed conserved but is zero due to a cancelation between two plain gravitational waves. This seems natural since nothing remains after a pair annihilation, and gives a hint on a physical interpretation of the conserved charge, which we call the gravitational charge. By modifying the space-time for the pair annihilation, we newly construct two types of a scattering plane gravitational wave and a pair creation of plane gravitational waves, and combining all, a Minkowski vacuum bottle, a Minkowski space-time surrounded by two moving plane gravitational waves.