Exact gravitational shock wave solution of higher order theories

We find an exact $\mathrm{pp}$-gravitational wave solution of the fourth-order gravity field equations. Outside the ($\delta$-like) source this is not a vacuum solution of general relativity. It represents the contribution of the massive, $m={(-\beta )}^{-\frac{1}{2}}$, spin-two field associated while the Ricci-squared term in the gravitational Lagrangian. The fourth-order terms tend to make the singularity of the curvature milder at the point where the particle is located. We generalize this analysis to $D$ dimensions, extended sources, and higher than fourth-order theories. We also briefly discuss the scattering of fields by these kinds of plane gravitational waves.