Shock Formation in Lovelock Theories

Abstract

We argue that Lovelock theories of gravity suffer from shock formation, unlike General Relativity. We consider the propagation of (i) a discontinuity in curvature, and (ii) weak, high frequency, gravitational waves. Such disturbances propagate along characteristic hypersurfaces of a "background" spacetime and their amplitude is governed by a transport equation. In GR the transport equation is linear. In Lovelock theories, it is nonlinear and its solutions can blow up, corresponding to the formation of a shock. We show that this effect is absent in some simple cases e.g. a flat background spacetime, and demonstrate its presence for a plane wave background. We comment on weak cosmic censorship, the evolution of shocks, and the nonlinear stability of Minkowski spacetime, in Lovelock theories.

arXiv comment43 pages, 5 figures

References in corpus (6)

• Viscosity Bound and Causality Violation
• Classification of the Weyl Tensor in Higher Dimensions
• Causality and Hyperbolicity of Lovelock Theories
• Causal Structures in Gauss-Bonnet gravity
• Gravitational solitons and $C^0$ vacuum metrics in five-dimensional Lovelock gravity
• Lagrangian Brane Dynamics in General Relativity and Einstein-Gauss-Bonnet Gravity

Cited by in corpus (25)

• Understanding photon sphere and black hole shadow in dynamically evolving spacetimes
• On the local well-posedness of Lovelock and Horndeski theories
• Towards the nonlinear regime in extensions to GR: assessing possible options
• Challenges to global solutions in Horndeski's theory
• Dynamics of Screening in Modified Gravity
• Causality in gravitational theories with second order equations of motion
• Generalized gravitational entropy without replica symmetry
• K-dynamics: well-posed 1+1 evolutions in K-essence
• Properties of ultra-compact particle-like solutions in Einstein-scalar-Gauss-Bonnet theories
• Lovelock black holes with non-constant curvature horizon
• Wave propagation and shock formation in the most general scalar-tensor theories
• A Survey of Black Hole Thermodynamics
• On the "Einstein-Gauss-Bonnet Gravity in Four Dimension"
• Fixing the dynamical evolution of self-interacting vector fields
• Einstein-Gauss-Bonnet black strings at large $\alpha$
• High-energy properties of the graviton scattering in quadratic gravity
• Characteristic analysis for integrable soliton models on two-dimensional target spaces
• $n+1$ formalism of $f($Lovelock$)$ gravity
• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• Numerical Relativity with Arbitrary Precision Arithmetic: Applications to Gravitational Collapse
• The well-posedness of the Cauchy problem for self-interacting vector fields
• The constraint equations of Lovelock gravity theories: a new ${\sigma }_k$-Yamabe problem
• Cherenkov radiation as ghost instability
• Stationary Stars Are Axisymmetric in Higher Curvature Gravity
• On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity