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.

Citation

Ohl, T., & Schenkel, A. (2009). Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes. Journal of High Energy Physics, 2009, Article JHEP01(2009)084. https://doi.org/10.1088/1126-6708/2009/01/084

• 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
• Electronic ISSN: 1029-8479
• 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