Exact Gravitational Shock Wave Solution of Higher Order Theories

TL;DR

This paper derives an exact gravitational wave solution in fourth order gravity theories, revealing how higher order terms influence singularity behavior and extending the analysis to higher dimensions and sources.

Contribution

It provides the first exact pp-wave solution in fourth order gravity, highlighting the effects of higher derivatives on gravitational wave properties and singularity structure.

Findings

Exact pp-wave solution in fourth order gravity

Higher order terms soften curvature singularities

Extension to higher dimensions and sources

Abstract

We find an {\it exact} pp--gravitational wave solution of the fourth order gravity field equations. Outside the (delta--like) source this {\it not} a vacuum solution of General Relativity. It represents the contribution of the massive, $m=(-\beta)^{-1/2}$, spin--two field associated to the Ricci squared term in the gravitational Lagrangian. The fourth order terms tend to make milder the singularity of the curvature 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 this kind of plane gravitational waves.