Local Well-posedness of Lovelock gravity

TL;DR

This paper establishes the local well-posedness of Lovelock gravity's initial value problem by demonstrating the equivalence of its field equations to a quasilinear PDE system, ensuring solutions depend continuously on initial data.

Contribution

It proves the local well-posedness of Lovelock gravity by linking its equations to a quasilinear PDE system, addressing a gap in understanding its dynamical properties.

Findings

Lovelock gravity admits a well-posed initial value problem.

Equivalence to a quasilinear PDE system facilitates analysis.

Analysis of the principal symbol confirms local well-posedness.

Abstract

It has long been known that Lovelock gravity, being of Cauchy-Kowalevskaya type, admits a well defined initial value problem for analytic data. However, this does not address the physically important issues of continuous dependence of the solution on the data and the domain of dependence property. In this note we fill this gap in our understanding of the (local) dynamics of the theory. We show that, by a known mathematical trick, the fully nonlinear harmonic-gauge-reduced Lovelock field equations can be made equivalent to a quasilinear PDE system. Due to this equivalence, an analysis of the principal symbol, as has appeared in recent works by other authors, is sufficient to decide the issue of local well-posedness of perturbations about a given background.