Canonical analysis and stability of Lanczos–Lovelock gravity

Abstract

We perform a spacetime 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.