2017/11/30 by Ram Brustein, Yotam Sherf · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Causality (physics) #Classical mechanics #Cosmology and Gravitation Theories #Einstein #General relativity #Mathematical physics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #String theory #Supergravity #Supersymmetry #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.97.084019
published as Phys. Rev. D 97, 084019 (2018) · Replaced to agree with the published version. Many typos corrected, text revised, results and conclusions unchanged
arxiv created 2018/04/10 · openalex publication_date 2018/04/16 · arxiv updated 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.