2016/08/31 by Giorgos Anastasiou, Rodrigo Olea
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Conformal gravity #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Curvature #Einstein #Einstein tensor #Einstein's constant #Equivalence (formal languages) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Riemann curvature tensor #Spacetime #Theoretical physics #Weyl tensor #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.94.086008
published as Phys. Rev. D 94, 086008 (2016) · Improved discussion on Einstein spaces in CG. Reference list updated. Final version for PRD
arxiv created 2016/10/22 · openalex publication_date 2016/10/26 · arxiv updated 2016/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We provide a simple derivation of the equivalence between Einstein and conformal gravity (CG) with Neumann boundary conditions given by Maldacena. As Einstein spacetimes are Bach flat, a generic solution to CG would contain both Einstein and non-Einstein parts. Using this decomposition of the spacetime curvature in the Weyl tensor makes manifest the equivalence between the two theories, both at the level of the action and the variation of it. As a consequence, we show that the on-shell action for critical gravity in four dimensions is given uniquely in terms of the Bach tensor.