On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations

TL;DR

This paper reviews properties of Einstein-Gauss-Bonnet gravity equations, focusing on their quasi-linearity and implications for the Cauchy problem and junction conditions in higher-dimensional models.

Contribution

It provides a detailed analysis of the quasi-linear nature of Einstein-Gauss-Bonnet equations and explores their effects in specific cosmological models.

Findings

Quasi-linearity influences the well-posedness of the Cauchy problem.

Junction conditions are affected by the quasi-linear structure.

Implications for higher-dimensional gravity models are discussed.

Abstract

We review some properties of the Einstein-"Gauss-Bonnet" equations for gravity--also called the Einstein-Lanczos equations in five and six dimensions, and the Lovelock equations in higher dimensions. We illustrate, by means of simple Kaluza-Klein and brane cosmological models, some consequences of the quasi-linearity of these equations on the Cauchy problem (a point first studied by Yvonne Choquet-Bruhat), as well as on "junction conditions".