Canonical Analysis and Stability of Lanczos-Lovelock Gravity

TL;DR

This paper analyzes the stability and Hamiltonian structure of Lanczos-Lovelock gravity in higher dimensions, revealing its dependence on curvature and showing that extended models are stable due to supersymmetry.

Contribution

It provides a detailed space-time analysis of Lanczos-Lovelock gravity, including constraints and stability properties, and clarifies the Hamiltonian formulation issues.

Findings

Pure LL has no Hamiltonian formulation.

Weak field constraints are not easily soluble.

Extended R+LL model is stable with positive energy.

Abstract

We perform a space-time analysis of the D>4 quadratic curvature Lanczos-Lovelock (LL) model, exhibiting its dependence on intrinsic/extrinsic curvatures, lapse and shifts. As expected from general covariance, the field equations include D constraints, of zeroth and first time derivative order. In the "linearized" - here necessarily cubic - limit, we give an explicit formulation in terms of the usual ADM metric decomposition, incidentally showing that time derivatives act only on its transverse-traceless spatial components. Unsurprisingly, pure LL has no Hamiltonian formulation, nor are even its - quadratic - weak field constraints easily soluble. Separately, we point out that the extended, more physical R+LL, model is stable - its energy is positive - due to its supersymmetric origin and ghost-freedom.