Geodesic deviation in pp-wave spacetimes of quadratic curvature gravity

TL;DR

This paper investigates the behavior of geodesic deviations in pp-wave spacetimes within quadratic curvature gravity, revealing new polarization modes of gravitational waves and analyzing an exact impulsive wave solution.

Contribution

It introduces a formulation of geodesic deviation in pp-wave spacetimes using Newman-Penrose scalars and identifies novel polarization modes in quadratic curvature gravity.

Findings

Quadratic curvature gravity pp-waves exhibit a transverse helicity-0 polarization.

They also retain two transverse helicity-2 polarizations similar to general relativity.

An exact impulsive wave solution demonstrates these polarization properties.

Abstract

We write the equation of geodesic deviations in the spacetime of $pp$-waves in terms of the Newman-Penrose scalars and apply it to study gravitational waves in quadratic curvature gravity. We show that quadratic curvature gravity $pp$-waves can have a transverse helicity-0 polarization mode and two transverse helicity-2 general relativity-like wave polarizations. A concrete example is given in which we analyze the wave polarizations of an exact impulsive gravitational wave solution to quadratic curvature gravity.