Local Well-posedness of Lovelock gravity

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.

arXiv comment2 pages, no figures. This article agrees with the published version apart from small corrections in equation 2 and text below equations 2 and 7

References in corpus (5)

• Lanczos-Lovelock models of gravity
• Causality and Hyperbolicity of Lovelock Theories
• Causal Structures in Gauss-Bonnet gravity
• Geometrodynamics of spherically symmetric Lovelock gravity
• Hamiltonian dynamics of Lovelock black holes with spherical symmetry

Cited by in corpus (9)

• Testing General Relativity with Present and Future Astrophysical Observations
• On the local well-posedness of Lovelock and Horndeski theories
• Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid
• Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory
• Holographic constraints on Bjorken hydrodynamics at finite coupling
• Slowly rotating black holes in Quasi-topological gravity
• Quasilinear reformulation of Lovelock gravity
• $n+1$ formalism of $f($Lovelock$)$ gravity
• The constraint equations of Lovelock gravity theories: a new ${\sigma }_k$-Yamabe problem