Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes

Ohl, Thorsten; Schenkel, Alexander

Abstract

As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations that are given by a twist of a Lie algebra acting on the spacetime manifold. We derive conditions on those twists that allow a given symmetry reduction. A complete classification of admissible deformations is possible in a class of twists generated by commuting vector fields. As examples, we explicitly construct the families of vector fields that generate twists which are compatible with Friedmann-Robertson-Walker cosmologies and Schwarzschild black holes, respectively. We find nontrivial isotropic twists of FRW cosmologies and nontrivial twists that are compatible with all classical symmetries of black hole solutions.

• Journal Article Type: Article
• Acceptance Date: Jan 9, 2009
• Online Publication Date: Jan 30, 2009
• Publication Date: Jan 30, 2009
• Deposit Date: Aug 22, 2019
• Journal: Journal of High Energy Physics
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 2009
• Article Number: JHEP01(2009)084
• DOI: https://doi.org/10.1088/1126-6708/2009/01/084
• Keywords: High Energy Physics - Theory; General Relativity and Quantum Cosmology
• Public URL: https://nottingham-repository.worktribe.com/output/2460620
• Publisher URL: https://iopscience.iop.org/article/10.1088/1126-6708/2009/01/084