Weyl gravity as general relativity

Abstract

When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.

Final version, 11 pages. The role of torsion is clarified, two appendices - on structure equations and Bianchi identities and on the basis equation - have been added

References in corpus (5)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Einstein Gravity from Conformal Gravity
• Fourth order Weyl gravity
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• Conformal Weyl gravity and perihelion precession

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• Tracing cosmic evolution through Weyl-Type f(Q,T) gravity model: theoretical analysis and observational validation
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• Cosmological Weyl-Einsteinian-Cubic Gravity as a Gauge Theory of Gravity
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• On the Near Horizon Canonical Quantum Microstates from $Ad{S}_2/CF{T}_1$ and Conformal Weyl Gravity
• Dynamical Implementation of the Constraints in Conformal Gravity
• Yang-Mills sources in biconformal gravity
• Geometry from geodesics: fine-tuning Ehlers, Pirani, and Schild
• A `Third' Quantization Constructed for Gauge Theory of Gravity