Noncommutative Geometry and Gravity

Abstract

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The class of noncommutative spaces studied is very rich. Non-anticommutative superspaces are also briefly considered. The differential geometry developed is covariant under deformed diffeomorphisms and it is coordinate independent. The main target of this work is the construction of Einstein's equations for gravity on noncommutative manifolds.

40pages; v2: references added

References in corpus (40)

• M Theory As A Matrix Model: A Conjecture
• The quantum structure of spacetime at the Planck scale and quantum fields
• Gravity coupled with matter and foundation of non-commutative geometry
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Non-commutative superspace from string theory
• Deforming Einstein's Gravity
• Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory
• Gravity in Non-Commutative Geometry
• Non(anti)commutative Superspace
• Noncommutative General Relativity
• Noncommutative Quantum Gravity
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• Cosmological perturbations and short distance physics from Noncommutative Geometry
• Some Aspects of Deformations of Supersymmetric Field Theories
• Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples
• An introduction to non-commutative differential geometry on quantum groups
• Extended jordanian twists for Lie algebras
• Twisting of quantum differentials and the Planck scale Hopf algebra
• Quantum Space-time and Classical Gravity
• Quantum symmetry groups of noncommutative spheres
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Noncommutative deformation of four dimensional Einstein gravity
• Differential Calculus on Iso_q (N), Quantum Poincare' Algebra and q - Gravity
• Bicovariant Quantum Algebras and Quantum Lie Algebras
• Chains of twists for classical Lie algebras
• Gauge and Einstein Gravity from Non-Abelian Gauge Models on Noncommutative Spaces
• Space-time symmetry of noncommutative field theory
• Quantum field theory and Hopf algebra cohomology
• The Lagrangian of q-Poincare' Gravity
• Twists and spectral triples for isospectral deformations
• Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces
• Bicovariant Calculus on Twisted ISO(N), Quantum Poincare' Group and Quantum Minkowski Space
• Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory
• Geometrical Tools for Quantum Euclidean Spaces
• R-Matrix Formulation of the Quantum Inhomogeneous Groups Iso_qr(N) and Isp_qr(N)
• Global Symmetries of Noncommutative Space-time
• Rieffel's deformation quantization and isospectral deformations

Cited by in corpus (241)

• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• Symmetry, Gravity and Noncommutativity
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Emergent Gravity from Noncommutative Gauge Theory
• Comments on noncommutative gravity
• Parameterized Post-Einsteinian Gravitational Waveforms in Various Modified Theories of Gravity
• Noncommutative Gravity
• The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Emergent Gravity from Noncommutative Spacetime
• Topics in Noncommutative Geometry Inspired Physics
• Twisted Gauge Theories
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Second Order Noncommutative Corrections to Gravity
• Noncommutative D=4 gravity coupled to fermions
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Noncommutative Gravity Solutions
• The Optical Appearance of Charged Four-Dimensional Gauss-Bonnet Black Hole with Strings Cloud and Non-Commutative Geometry Surrounded by Various Accretions Profiles
• Constraining non-commutative space-time from GW150914
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Noncommutative field theory with the Wick-Voros product
• An introduction to quantum gravity
• On The Correspondence Between Noncommuative Field Theory And Gravity
• Noncommutative BTZ Black Hole and Discrete Time
• Noncommutative supergravity in D=3 and D=4
• Remarks on twisted noncommutative quantum field theory
• Gravity and the Structure of Noncommutative Algebras
• Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations
• Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
• Geodesic equation in $k$-Minkowski spacetime
• Noncommutative corrections to classical black holes
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• kappa-deformed Spacetime From Twist
• Noncommutative gravity at second order via Seiberg-Witten map
• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• Noncommutativity and Non-anticommutativity in Perturbative Quantum Gravity
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Noncommutative $D_3$-brane, Black Holes and Attractor Mechanism
• Newton's Equation on the kappa space-time and the Kepler problem
• Instantons and Emergent Geometry
• Tunneling between de Sitter and anti de Sitter black holes in a noncommutative D3-brane formalism
• $\kappa$-deformed Dirac Equation
• Twist as a Symmetry Principle and the Noncommutative Gauge Theory Formulation
• Spherically Symmetric Noncommutative Space: d = 4
• On Noncommutative Minisuperspace and the Friedmann equations
• Noncommutative Field Theory from twisted Fock space
• Noncommutative Symmetries and Gravity
• The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity
• Hermitian versus non-Hermitian representations for minimal length uncertainty relations
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Riemannian Geometry of Noncommutative Surfaces
• Gauge theories on quantum spaces
• Finite field-dependent symmetries in perturbative quantum gravity
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Effects of Noncommutativity on the Black Hole Entropy
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Noncommutative correction to the entropy of Schwarzschild black hole with GUP
• Tunneling of massive particles from noncommutative inspired Schwarzschild black hole
• Noncommutative minisuperspace, gravity-driven acceleration and kinetic inflation
• On second quantization on noncommutative spaces with twisted symmetries
• Quantum Fields with Noncommutative Target Spaces
• Twisted Covariant Noncommutative Self-dual Gravity
• On possible wormhole solutions supported by non-commutative geometry within $f(R,L_m)$ gravity
• Nonassociative differential geometry and gravity with non-geometric fluxes
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Twisted Poincare Invariance, Noncommutative Gauge Theories and UV-IR Mixing
• Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
• Noncommutative BTZ Black Hole in Polar Coordinates
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Triproducts, nonassociative star products and geometry of R-flux string compactifications
• Effects of deformed phase space on scalar field cosmology
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Noncommutative SO(2,3) gauge theory and noncommutative gravity
• Kappa-Deformations: Historical Developments and Recent Results
• Quantum statistics and noncommutative black holes
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• Exploring wormhole solutions in curvature-matter coupling gravity supported by noncommutative geometry and conformal symmetry
• Gravitational amplitudes in black-hole evaporation: the effect of non-commutative geometry
• Towards A Background Independent Quantum Gravity
• AdS-inspired noncommutative gravity on the Moyal plane
• Geodesic equation in non-commutative gauge theory of gravity
• Noncommutative Einstein-Maxwell pp-waves
• Towards a Theory of Nonassociative Gravity
• Braided Cartan Calculi and Submanifold Algebras
• Braided Symmetries in Noncommutative Field Theory
• Non-singular Brans-Dicke collapse in deformed phase space
• Emergence of Geometric phase shift in Planar Non-commutative Quantum Mechanics
• Quasinormal Modes in Noncommutative Schwarzschild black holes
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• On some models of geometric noncommutative general relativity
• Perturbative quantum gravity in Batalin-Vilkovisky formalism
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Test of Emergent Gravity
• Diffeomorphism covariant star products and noncommutative gravity
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Notes on "quantum gravity" and non-commutative geometry
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Field Theory on Nonanticommutative Superspace
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Quantum tunneling and spectroscopy of noncommutative inspired Kerr black hole
• Noncommutative fields and actions of twisted Poincare algebra
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Quantization of Emergent Gravity
• Field Theory on Curved Noncommutative Spacetimes
• Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Deformed Phase Space Kaluza-Klein cosmology and late time acceleration
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Noncommutative principal bundles through twist deformation
• Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes
• Noncommutative brane-world, (Anti) de Sitter vacua and extra dimensions
• SL(2,C) gravity on noncommutative space with Poisson structure
• Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves
• N=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras
• Noncommutative gravity and the relevance of the $\theta$-constant deformation
• Relating Noncommutative SO(2,3) Gravity to the Lorentz-Violating Standard-Model Extension
• Quantum gravity on polygons and $\mathbb{R}\times {\mathbb{Z}}_n$ FLRW model
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Dispersion Relations in $\kappa$-Noncommutative Cosmology
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• Metric perturbations in Noncommutative Gravity
• Conformally symmetric wormhole solutions supported by non-commutative geometry in $f(Q,T)$ gravity
• Duality and Braiding in Twisted Quantum Field Theory
• Noncommutative gravity with self-dual variables
• Fuzzy and discrete black hole models
• Noncommutative field gas driven inflation
• On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
• Noncommutative correction to the entropy of charged BTZ black hole
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Noncommutativity from spectral flow
• Reality in Noncommutative Gravity
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• Deformed Gauge Theories
• Extending general covariance: Moyal-type noncommutative manifolds
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Breakdown of Lorentz Invariance for Spin-1/2 Particle Motion in Curved Space-Time with Applications to Muon Decay
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• Green's Functions in Perturbative Quantum Gravity
• Thermofield dynamics and Gravity
• Time-space noncommutativity and Casimir effect
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Exploring the thermodynamics of non-commutative scalar fields
• On the Entropy of Deformed Phase Space Black Hole and the Cosmological Constant
• Noncommutative Gravity and the *-Lie algebra of diffeomorphisms
• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• Quantum entropy couples matter with geometry
• From Peierls brackets to a generalized Moyal bracket for type-I gauge theories
• Twisting all the way: from algebras to morphisms and connections
• Absorption cross section in gravity's rainbow from confluent Heun equation
• Cartan structure equations and Levi-Civita connection in noncommutative geometry
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle
• Gravitational collapse of spherically symmetric stars in noncommutative general relativity
• A Variational Formulation of Symplectic Noncommutative Mechanics
• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations
• Noncommutative Solitons of Gravity
• Thermodynamical properties of a noncommutative anti-de Sitter-Einstein-Born-Infeld spacetime from gauge theory of gravity
• Regular Black Holes and Noncommutative Geometry Inspired Fuzzy Sources
• Gravitational probe of quantum spacetime
• Twisted submanifolds of R^n
• U(2,2) gravity on noncommutative space with symplectic structure
• Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics
• D-deformed Wess-Zumino model and its renormalizability properties
• Star Product Geometries
• Twist star products and Morita equivalence
• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• BV quantization of dynamical fuzzy spectral triples
• Noncommutative quasinormal modes of Schwarzschild black hole
• (Non)renormalizability of the D-deformed Wess-Zumino model
• Laplacians on Fuzzy Riemann Surfaces
• The Moyal Sphere
• High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Twist Quantization of String and B Field Background
• Maximal acceleration in non-commutative space-time and its implications
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Harmonic oscillator in twisted Moyal plane: eigenvalue problem and relevant properties
• Newtonian cosmology and Evolution of kappa-deformed universe
• Noncommutative Reissner-Nordstrøm Black hole
• BMS algebras in 4 and 3 dimensions, their quantum deformations and duals
• Angles in Fuzzy Disc and Angular Noncommutative Solitons
• Differential calculus and gauge transformations on a deformed space
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Mapping spaces and automorphism groups of toric noncommutative spaces
• Gravity in Extreme Regions Based on Noncommutative Quantization of Teleparallel Gravity
• The scalar wave equation in a non-commutative spherically symmetric space-time
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Twisted Quadrics and Algebraic Submanifolds in ${\mathbb{R}}^n$
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Superradiance scattering of scalar, electromagnetic, and gravitational fields and thin accretion disk around non-commutating Kerr black hole
• Neutron Star in Quantized-space-time
• How does Casimir energy fall in $\kappa$-deformed space-time?
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Spacetime Noncommutativity in Models with Warped Extradimensions
• Deformation quantization of principal bundles
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• On Light-like Deformations of the Poincaré Algebra
• Learning from Julius' star, *, $\star$
• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
• Field Theory with Coordinate Dependent Noncommutativity
• T-Minkowski noncommutative spacetimes II: classical field theory
• Module parallel transports in fuzzy gauge theory
• Diffeomorphisms on Fuzzy Sphere
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Commutative deformations of general relativity: nonlocality, causality, and dark matter
• Quantum Spacetime Pictures and Dynamics from a Relativity Perspective
• Imprints of non-commutativity on charged black holes
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• Quantisation of $\kappa$-deformed Dirac equation
• Dirac Operators on Noncommutative Curved Spacetimes
• Twisted SUSY: twisted symmetry versus renormalizability
• Non-commutative correction of ideal gas thermodynamics
• QFT on homothetic Killing twist deformed curved spacetimes
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Generalized symmetries as homotopy Lie algebras
• Signatures of Noncommutative Geometry in Muon Decay for Nonsymmetric Gravity
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
• Holographic Entanglement Entropy for noncommutative Anti-de Sitter space
• Local Space-Time Curvature Effects on Quantum Orbital Angular Momentum
• Entropy of black holes, charged probes and noncommutative generalization
• Super Yang-Mills Theory from a Supermatrix Model
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects
• A Perfectoid Duality Between M-Theory and F-Theory
• A bigravity model from noncommutative geometry
• Covariant Star Product on Semi-Conformally Flat Noncommutative Calabi-Yau Manifolds and Noncommutative Topological Index Theorem
• Gravitational-wave constraints on noncommutative spacetime from GW190814
• N=1/2 Global SUSY: R-Matrix Approach
• Nonperturbative deformation of D-brane states by the world sheet noncommutativity