Curvature-singularity-free solutions for colliding plane gravitational waves with brokenu-vsymmetry

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Abstract
We discuss the most general solution describing the collision of plane gravitational waves with constant polarization. Among these solutions there is an infinite-dimensional family of metrics free of curvature singularities and analytically extendable across the ‘‘focusing’’ hypersurface. These regular solutions describe collisions between two incoming plane waves with different amplitudes for which u-v symmetry is broken. Boundary conditions on the null hypersurfaces u=0, v=0 are discussed and it is shown that any solution describing the scattering of plane gravitational waves with constant polarization has to include at least two solitary terms each of which stabilizes the behavior of the gravitational field on the null boundaries.

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