Metric perturbations in noncommutative gravity

A bstract We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construc...

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Bibliographic Details
Published in:The journal of high energy physics 2024-06, Vol.2024 (6), p.130-32, Article 130
Main Authors: Herceg, Nikola, Jurić, Tajron, Samsarov, Andjelo, Smolić, Ivica
Format: Article
Language:English
Subjects:
Algebra
Black Holes
Classical and Quantum Gravitation
Collaboration
Deformation
Differential geometry
Elementary Particles
Geometry
Gravitation theory
Gravitational waves
Gravity
Isomorphism
Models of Quantum Gravity
Non-Commutative Geometry
Perturbation theory
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Radiation
Regular Article - Theoretical Physics
Relativity Theory
Space-Time Symmetries
Spectrum analysis
Stars & galaxies
String Theory
Theory of relativity
Universe
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Summary:A bstract We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construction is a general formalism for obtaining NC corrections to the classical theory of gravity for a wide class of deformations and a general background. This also includes a novel proposal for noncommutative Einstein manifold. Moreover, the general construction is applied to the case of a linearized gravitational perturbation theory to describe a NC deformation of the metric perturbations. We specifically present an example for the Schwarzschild background and axial perturbations, which gives rise to a generalization of the work by Regge and Wheeler. All calculations are performed up to first order in perturbation of the metric and noncommutativity parameter. The main result is the noncommutative Regge-Wheeler potential. Finally, we comment on some differences in properties between the Regge-Wheeler potential and its noncommutative counterpart.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP06(2024)130