2018/06/30 by Marco de Cesare, Mairi Sakellariadou, Patrizia Vitale
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Commutative property #Cosmology and Gravitation Theories #Curvature #Gauge theory #Geometry #Gravitation #Mathematical physics #Minkowski space #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum mechanics #Spacetime #Tetrad #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/1361-6382/aae3f5
published as Class. Quantum Grav. 35 (2018) 215009 · 52 pages; v2: added references, corrected minor typos; matches published version
openalex publication_date 2018/09/25 · arxiv created 2018/10/19 · arxiv updated 2018/10/22 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06
Abstract We build a noncommutative extension of Palatini–Holst theory on a twist-deformed spacetime, generalizing a model that has been previously proposed by Aschieri and Castellani. The twist deformation entails an enlargement of the gauge group, and leads to the introduction of new gravitational degrees of freedom. In particular, the tetrad degrees of freedom must be doubled, thus leading to a bitetrad theory of gravity. The model is shown to exhibit new duality symmetries. The introduction of the Holst term leads to a dramatic simplification of the dynamics, which is achieved when the Barbero–Immirzi parameter takes the value , corresponding to a self-dual action. We study in detail the commutative limit of the model, focusing in particular on the role of torsion and non-metricity. The effects of spacetime noncommutativity are taken into account perturbatively, and are computed explicitly in a simple example. Connections with bimetric theories and the role of local conformal invariance in the commutative limit are also explored.