Causal properties of nonlinear gravitational waves in modified gravity

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 a2 of the Taylor expansion of f(R) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values..