A MacDowell-Mansouri type formulation for Einstein manifolds

2023/04/12 by José Eduardo Rosales Quintero, Quintero, José Eduardo Rosales
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.2304.05606

openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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