Shock Formation in Lovelock Theories

TL;DR

Lovelock theories of gravity can develop shocks due to nonlinear propagation of disturbances, unlike General Relativity, which may impact their stability and cosmic censorship.

Contribution

This paper demonstrates that Lovelock gravity theories can form shocks through nonlinear wave propagation, a phenomenon absent in General Relativity.

Findings

Shock formation occurs in Lovelock theories with certain backgrounds.

Shock formation is absent in flat spacetime but present in plane wave backgrounds.

Implications for cosmic censorship and stability 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.