NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion

Abstract

Noncommutative (NC) gravity is constructed on the canonical noncommutative (Moyal-Weyl) space-time as a noncommutative $SO(2,3{)}_{\star }$ gauge theory. The NC gravity action consists of three different terms: the first term is of Mac-Dowell Mansouri type, while the other two are generalizations of the Einstein-Hilbert action and the cosmological constant term. The expanded NC gravity action is then calculated using the Seiberg-Witten (SW) map and the expansion is done up second order in the deformation parameter. We analyze in details the low energy sector of the full model. We calculate the equations of motion, discuss their general properties and present one solution: the NC correction to Minkowski space-time. Using this solution, we explain breaking of the diffeomorphism symmetry as a consequence of working in a particular coordinate system given by the Fermi normal coordinates.

arXiv comment26 pages, no figures

References in corpus (42)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• String Theory and Noncommutative Geometry
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Quantum Gravity at a Lifshitz Point
• Data Tables for Lorentz and CPT Violation
• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Membranes at Quantum Criticality
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Noncommutative Geometry and Gravity
• The Standard Model on Non-Commutative Space-Time
• Construction of non-Abelian gauge theories on noncommutative spaces
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Deforming Einstein's Gravity
• Search for resonances in diphoton events at $\sqrt{s}$=13 TeV with the ATLAS detector
• Renormalization of Lorentz violating theories
• The Z -> gamma gamma, gg Decays in the Noncommutative Standard Model
• Search for resonant production of high-mass photon pairs in proton-proton collisions at sqrt(s) = 8 and 13 TeV
• Riemann-Einstein Structure from Volume and Gauge Symmetry
• Noncommutative Gravity
• Emergent Gravity from Noncommutative Spacetime
• Noncommutative D=4 gravity coupled to fermions
• Noncommutative Gravity Solutions
• Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
• Improved Z -> gamma gamma decay in the renormalizable gauge sector of the noncommutative standard model
• Noncommutative deformation of four dimensional Einstein gravity
• Constraining non-commutative space-time from GW150914
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Cosmological solutions of emergent noncommutative gravity
• Noncommutative supergravity in D=3 and D=4
• Gravity and the Structure of Noncommutative Algebras
• The Energy-momentum of a Poisson structure
• Spherically Symmetric Noncommutative Space: d = 4
• Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies
• Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologies
• Noncommutative SO(2,3) gauge theory and noncommutative gravity
• AdS-inspired noncommutative gravity on the Moyal plane
• Classical Noncommutative Electrodynamics with External Source
• On some models of geometric noncommutative general relativity
• Noncommutative gravity and the relevance of the $\theta$-constant deformation
• Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle

Cited by in corpus (25)

• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Noncommutative scalar field in the non-extremal Reissner-Nordström background: QNM spectrum
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Braided Symmetries in Noncommutative Field Theory
• Higher-spin gravity and torsion on quantized space-time in matrix models
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Relating Noncommutative SO(2,3) Gravity to the Lorentz-Violating Standard-Model Extension
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Metric perturbations in Noncommutative Gravity
• Noncommutative gravity with self-dual variables
• Charged rotating BTZ black holes in noncommutative spaces and torsion gravity
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Intertwining noncommutativity with gravity and particle physics
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Proposal for a new quantum theory of gravity
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Gravity in Extreme Regions Based on Noncommutative Quantization of Teleparallel Gravity
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Noncommutative Gauge Theories and Gravity
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
• A bigravity model from noncommutative geometry
• Gauge Theories on Fuzzy Spaces and Gravity