$\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit

Abstract

We employ a twist deformation of infinitesimal diffeomorphisms to construct a modification of General Relativity on a non-commutative spacetime extending the local kappa-Minkowski geometry. This spacetime arises in Deformed Special Relativity (DSR) models, where a fundamental length scale is incorporated into Special Relativity as an effective description of quantum gravitational effects. To avoid the mathematical and physical inconsistencies associated with twisting the Poincare group, we instead deform the dilatation-enlarged IGL(3,1) group, constructing a covariant and explicitly consistent gravitational theory (distinct from Weyl gravity). The relativistic consistency of the twisted kappa-Minkowski spacetime is demonstrated, including deformed transformations and differential structures. A physically motivated Inonu-Wigner (IW) contraction procedure is suggested to enable a well-defined classical limit, addressing the correspondence issue. This framework provides a consistent foundation for a dynamical sector of DSR and allows, in future treatment, explicit computations that could advance phenomenological predictions.

arXiv comment36 pages, 1 table, published version

References in corpus (48)

• Deformation quantization of Poisson manifolds, I
• Quantum gravity and minimum length
• General relativity as an effective field theory: The leading quantum corrections
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Minimal Length Scale Scenarios for Quantum Gravity
• Generalized Lorentz invariance with an invariant energy scale
• Gauge Theory on Noncommutative Spaces
• A Gravity Theory on Noncommutative Spaces
• The principle of relative locality
• Noncommutative Geometry and Gravity
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Non-commutative space-time of Doubly Special Relativity theories
• Quantum group gauge theory on quantum spaces
• Kappa-Minkowski space-time and the star product realizations
• Noncommutative ${\Phi }^4$ Theory at Two Loops
• Waves on Noncommutative Spacetime and Gamma-Ray Bursts
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Taming nonlocality in theories with Planck-scale-deformed Lorentz symmetry
• Quantum and Braided Linear Algebra
• Noncommutative D=4 gravity coupled to fermions
• Noncommutative Gravity Solutions
• Twisting of quantum differentials and the Planck scale Hopf algebra
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Space-time symmetry of noncommutative field theory
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• Comments on the Energy-Momentum Tensor in Non-Commutative Field Theories
• kappa-deformed Spacetime From Twist
• A non-commutative Minkowskian spacetime from a quantum AdS algebra
• Bicovariant Calculus on Twisted ISO(N), Quantum Poincare' Group and Quantum Minkowski Space
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• A twisted look on kappa-Minkowski: U(1) gauge theory
• A symmetry invariant integral on kappa-deformed spacetime
• Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
• Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski
• Twisting and kappa-Poincare
• Noncommutative spaces of worldlines
• Comparison of relativity theories with observer-independent scales of both velocity and length/mass
• Curved momentum space, locality, and generalized space-time
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Does a deformation of special relativity imply energy dependent photon time delays?
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• The Energy-Momentum Tensor in Noncommutative Gauge Field Models
• On the 5D differential calculus and translation transformations in 4D kappa-Minkowski noncommutative spacetime
• Metric perturbations in Noncommutative Gravity
• On the energy-momentum tensor in Moyal space

Cited by in corpus (2)

• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes
• $\kappa$-General-Relativity II: An Astrophysical Observable from a 2-Body system