A MacDowell-Mansouri type formulation for Einstein manifolds
Abstract
We study a pure connection formulation plus algebraic constraints in four spacetime dimensions where the gauge group G ⊃ SO(1, 3). We show that the action has, as particular cases, the MacDowell-Mansouri and the Stelle-West formulations for gravity. Also, under adequate specification of the constraint terms, we obtain Einstein manifolds, i.e., torsionless conformally flat manifolds.
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