On Swift Gravitons

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