On Swift Gravitons

TL;DR

The work investigates local causal structure and swift graviton propagation in higher-curvature gravity theories by analyzing a probe graviton on a pp-wave background generated by axisymmetric beams. Using the method of characteristics, it shows that many $[R^2]$, $[R^3]$, and $[R\nabla^2 R]$ terms either preserve GR-like causality or induce swift propagation depending on polarization and scale, while $[R^4]$ terms can create degenerate hyperbolicity that is fixable by including appropriate $[R^3]$ corrections. In dimensions $D>4$ the presence of swift propagation largely does not depend on coupling signs, whereas in $D=4$ the signs can crucially affect swiftness; Gauss-Bonnet is a notable exception with nontrivial swift behavior. The results place causality-based constraints on viable extended gravity theories and highlight the role of hyperbolicity and initial-value well-posedness in assessing higher-curvature models, with implications for string theory-inspired effective actions and their UV completions.

Abstract

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$)^3$, $\nabla^2 ($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.