Causal properties of nonlinear gravitational waves in modified gravity

TL;DR

This paper derives exact nonlinear gravitational wave solutions in polynomial $f(R)$ gravity, revealing differences in causality and superluminal phenomena compared to general relativity, with potential astrophysical implications.

Contribution

It provides the first exact nonlinear vacuum solutions in polynomial $f(R)$ gravity, analyzing their causal structure and stability.

Findings

Boundaries of gravitational dependence are not null in $f(R)$ gravity.

Solutions can be superluminal for all quadratic coefficients.

Existence of anisotropic solutions with complex wave-fronts.

Abstract

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient $a_{2}$ of the Taylor expansion of $f(R)$ is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of $a_{2}$. Anisotropic solutions are found, whose wave-fronts trace out time- or space-like hypersurfaces with complicated geometric properties. We show that the solutions exist in $f(R)$ theories that are consistent with Solar System and pulsar timing experiments.