Metric perturbations in noncommutative gravity

• 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
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2024)130

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.