Non-commutative Geometry from Perturbative Quantum Gravity

Abstract

Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where perturbative quantum gravity provides a predictive framework? Moreover, is it necessary to introduce non-commutativity by hand, or does it arise through quantum-gravitational effects? We show that the first question can be answered in the affirmative, and the second one in the negative: perturbative quantum gravity predicts non-commutativity at the Planck scale, once one clarifies the structure of observables in the quantum theory.

10 pages, matches published version

References in corpus (8)

• Universality of Quantum Gravity Corrections
• GUP parameter from quantum corrections to the Newtonian potential
• Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
• Wedge-Local Quantum Fields and Noncommutative Minkowski Space
• One-loop gravitational wave spectrum in de Sitter spacetime
• An intrinsic characterization of the Kerr metric
• The $\kappa$-(A)dS noncommutative spacetime
• Wedge-Local Quantum Fields on a Nonconstant Noncommutative Spacetime

Cited by in corpus (16)

• Exploring Non--commutativity as a Perturbation in the Schwarzschild Black Hole: Quasinormal Modes, Scattering, and Shadows
• Thermodynamics of Schwarzschild-AdS black hole in non-commutative geometry
• Visions in Quantum Gravity
• Perturbative quantum evolution of the gravitational state and dressing in general backgrounds
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Non-commutative Geometry from Perturbative Quantum Gravity in de Sitter spacetime
• Thermodynamics of high order correction for Schwarzschild-AdS black hole in non-commutative geometry
• Lectures in Quantum Gravity
• Thermodynamic phase transition and Joule-Thomson expansion of a quantum corrected black hole in AdS spacetime
• Estimating the strength of Lorentzian distribution in non-commutative geometry by solar system tests
• Non-commutative coordinates from quantum gravity
• Linearization (in)stabilities and crossed products
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
• Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
• Curvature, area and Gauss-Bonnet formula of the Moyal sphere
• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes