• Open Access

Causality violations in Lovelock theories

Ram Brustein and Yotam Sherf
Phys. Rev. D 97, 084019 – Published 16 April 2018

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.

  • Received 5 December 2017

DOI:https://doi.org/10.1103/PhysRevD.97.084019

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Ram Brustein* and Yotam Sherf

  • Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel

  • *ramyb@bgu.ac.il
  • sherfyo@post.bgu.ac.il

Article Text

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Issue

Vol. 97, Iss. 8 — 15 April 2018

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