On gravitational shock waves

The discontinuity planes of the Riemann curvature tensorR_klmⁱ in the Einsteinian vacuumR_kl=0 are isotropic hypersurfaces. These surfaces are to be conceived as being constructed of lightlike geodesics, which form, in the eikonal approximation, gravitational radiation. The discontinuity planes themselves describe the wave fronts of disturbances of the metricg_ik, propagating with the velocity of light. By successively applying continuity conditions for the derivatives of theg_ik that follow from Einstein's equations, we obtain the universal expression of gravitational wave fields in space-time strips (or representations) of arbitrarily selected Einstein spaces.