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From conformal to Einstein Gravity

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arxiv 1608.07826 v2 pith:CHX6WCF4 submitted 2016-08-28 hep-th gr-qc

Giorgos Anastasiou , Rodrigo Olea This is my paper · ORCID
classification hep-thgr-qc
keywords einsteingravityactionbachconformalequivalencegiventensor
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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 part. 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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Conformal Renormalisation of 8D Einstein Gravity

    hep-th 2026-07 accept novelty 7.0 of 10

    Holographic renormalisation of 8D Einstein-AdS gravity is recovered as the Einstein sector of the unique conformal gravity admitting constant-negative-curvature Einstein solutions, with matching counterterms.

  2. Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs

    hep-th 2019-08 conditional novelty 6.0 of 10

    Kounterterm renormalization is extended to even-dimensional holographic CFTs, yielding a universal entanglement entropy formula whose logarithmic coefficient reproduces the type A central charge.

  3. Conformal Gravity and Transformations in the Symmetric Teleparallel Framework

    gr-qc 2019-08 conditional novelty 6.0 of 10

    A conformally invariant gravity action built from the square of a non-metricity scalar gives second-order field equations in symmetric teleparallel gravity.

  4. Renormalized pseudoentropy in dS/CFT

    hep-th 2026-02 conditional novelty 5.0 of 10

    Renormalized holographic pseudoentropy in dS/CFT is constructed from conformal-gravity actions in four and six dimensions, yielding finite sphere values and Mezei-like shape dependence for small deformations.

  5. From the Unification of Conformal and Fuzzy Gravities with Internal Interactions to the $SO(10)$ GUT and the Particle Physics Standard Model

    hep-th 2024-12 conditional novelty 4.0 of 10

    One-loop gauge coupling running gives intermediate scales from 10^10 to 10^13 GeV and GUT scales from 10^15 to 2x10^16 GeV for four SO(10) breaking chains of the conformal-gravity unification, with two high-scale scen...

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