2012/04/18 by Diego Gonzalez, Diego González, Merced Montesinos +6 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Sensor Technology #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #gr-qc #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.1204.4225
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openalex publication_date 2012/04/18 · arxiv created 2013/01/24 · arxiv updated 2013/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Plebanski formulation of complex general relativity is given in terms of variables valued in the complexification of the so(3) Lie algebra. Therefore, it is genuinely a gauge theory that is also diffeomorphism-invariant. For this reason, the way that the Levi-Civita connection emerges from this formulation is not direct because both the internal (gauge) and the spacetime connections are geometrical structures a priori not related, there is not a natural link between them. Any possible relationship must be put in by hand or must come from extra hypotheses. In this paper, we analyze the correct relationship between these connections and show how they are related.