2005/04/30 by Paolo Aschieri, Christian Blohmann, Marija Dimitrijević Ćirić +4 · 9 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/22/17/011
published as Class.Quant.Grav. 22 (2005) 3511-3532 · 28 pages, v2: coefficient in equ. (10.15) corrected, references added, v3: references added, published version
openalex publication_date 2005/08/10 · arxiv created 2005/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter θ. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra, a covariant tensor calculus is constructed and all the concepts such as metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a θ-deformed Einstein–Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in θ.