Superluminal graviton propagation

We use the method of characteristics to study superluminal graviton (which we call the swift graviton) propagation in theories of higher-curvature gravity of the form $(\text{Riemann}{)}^2$, $(\text{Riemann}{)}^3$, ${\nabla }^2(\text{Riemann}{)}^2$ and $(\text{Riemann}{)}^4$. We consider a $pp$-wave background. When probed by gravitons with an appropriate polarization, several of the gravitational theories under consideration exhibit characteristic hypersurfaces outside the flat spacetime light cone.