Canonical Analysis and Stability of Lanczos-Lovelock Gravity

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.

amplified, published version; section added on positive energy of R+LL

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• Pure Lovelock gravity and Chern-Simons theory
• f(Lovelock) theories of gravity
• Lovelock gravities from Born-Infeld gravity theory
• Generalized Pure Lovelock Gravity
• 1/r potential in higher dimensions
• Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity
• Spectra, vacua and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes
• Connecting Holographic Wess--Zumino Consistency Conditions to the Holographic Anomaly
• Hamiltonian dynamics of Lovelock black holes with spherical symmetry
• History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term
• Early universe in view of a modified theory of gravity
• The issue of Branched Hamiltonian in F(T) Teleparallel Gravity
• Inflation and cosmological evolution with $F(R,G)$ gravity theory
• Griffiths Variational Multisymplectic Formulation for Lovelock Gravity
• Conserved quantities for black hole solutions in pure Lovelock gravity
• Conflict between some higher-order curvature invariant terms