Noncommutative gravity and the relevance of the $\theta$-constant deformation

Abstract

In this Letter we construct the noncommutative (NC) gravity model on the $\theta$-constant NC space-time. We start from the NC $SO(2,3{)}_{\star }$ gauge theory and use the enveloping algebra approach and the Seiberg-Witten map to construct the effective NC gravity action. The action and the equations of motion are expanded up to second order in the deformation parameter. The equations of motion show that the noncommutativity plays a role of a source for the curvature and/or torsion. Finally, we calculate the NC corrections to the Minkowski space-time and we show that in the presence of noncommutativity Minkowski space-time becomes curved, but remains torsion-free. The breaking of diffeomorphism invariance is understood in terms of the preferred coordinate system. We show that the coordinates we are using are the Fermi normal coordinates. This suggests that the natural coordinate system in which one should study NC gravity is given by the Fermi normal coordinates.

5 pages

References in corpus (28)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• String Theory and Noncommutative Geometry
• The quantum structure of spacetime at the Planck scale and quantum fields
• The motion of point particles in curved spacetime
• 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
• 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
• Riemann-Einstein Structure from Volume and Gauge Symmetry
• Emergent Gravity from Noncommutative Spacetime
• Noncommutative D=4 gravity coupled to fermions
• Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
• Noncommutative deformation of four dimensional Einstein gravity
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Gravity and the Structure of Noncommutative Algebras
• Seiberg--Witten Maps to All Orders
• Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
• Noncommutative gravity at second order via Seiberg-Witten map
• 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
• On noncommutative spherically symmetric spaces

Cited by in corpus (11)

• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• Noncommutative scalar field in the non-extremal Reissner-Nordström background: QNM spectrum
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Gravity in Extreme Regions Based on Noncommutative Quantization of Teleparallel Gravity
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly