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

Authors
  • Ohl, Thorsten
  • Schenkel, Alexander
Type
Published Article
Publication Date
Jan 29, 2009
Submission Date
Oct 27, 2008
Identifiers
DOI: 10.1088/1126-6708/2009/01/084
Source
arXiv
License
Yellow
External links

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.

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