2013/11/30 by Josef Klusoň, J. Klusoň, Markku Oksanen +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conformal gravity #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Curvature #Gauge theory #General relativity #Geometry #Gravitation #Graviton #Lorentz covariance #Lorentz transformation #Massive gravity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Riemann curvature tensor #Scalar curvature #Spacetime #Theoretical physics #Weyl tensor #Weyl transformation #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.89.064043
published as Phys.Rev.D89:064043,2014 · 45 pages. v2: Improved comparison to previous results, five new references, discussion on alternative formulations included, to be published in Phys. Rev. D
arxiv created 2014/02/28 · openalex publication_date 2014/03/18 · arxiv updated 2014/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable---a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.