2011/10/31 by S. Deser, S Deser, J. Franklin +1 · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Derivative (finance) #Gravitation #Gravitational field #Hamiltonian (control theory) #Metric (unit) #Noncommutative and Quantum Gravity Theories #Quadratic equation #Stability (learning theory) #Time derivative #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/29/7/072001
published as Class. Quantum Grav. 29 (2012) 072001 · amplified, published version; section added on positive energy of R+LL
openalex publication_date 2012/02/24 · arxiv created 2012/03/01 · arxiv updated 2012/03/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.