Causality Violations in Lovelock Theories

TL;DR

This paper investigates causality constraints in Lovelock gravity theories, revealing that significant modifications to general relativity lead to non-Lorentzian effective metrics, thus limiting Lovelock theories to perturbative extensions of GR.

Contribution

It provides a general expression for the effective metric in Lovelock theories and demonstrates that causality constraints restrict these theories to small deviations from GR.

Findings

Effective metric is Lorentzian for small Lovelock modifications.

Lovelock theories are limited to perturbative regimes due to causality constraints.

Results align with previous studies on causality in higher-derivative gravity.

Abstract

Higher-derivative gravity theories, such as Lovelock theories, generalize Einstein's general relativity (GR). Modifications to GR are expected when curvatures are near Planckian and appear in string theory or supergravity. But can such theories describe gravity on length scales much larger than the Planck cutoff length scale? Here we find causality constraints on Lovelock theories that arise from the requirement that the equations of motion (EOM) of perturbations be hyperbolic. We find a general expression for the "effective metric" in field space when Lovelock theories are perturbed around some symmetric background solution. In particular, we calculate explicitly the effective metric for a general Lovelock theory perturbed around cosmological Friedman-Robertson-Walker backgrounds and for some specific cases when perturbed around Schwarzschild-like solutions. For the EOM to be hyperbolic, the effective metric needs to be Lorentzian. We find that, unlike for GR, the effective metric is generically not Lorentzian when the Lovelock modifications are significant. So, we conclude that Lovelock theories can only be considered as perturbative extensions of GR and not as truly modified theories of gravity. We compare our results to those in the literature and find that they agree with and reproduce the results of previous studies.