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

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.

LaTeX, 20 pages, no figures, minor modifications, reference added, to appear in JHEP

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• Noncommutative Gravity Solutions
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
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