Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
arXiv:0810.4885 · doi:10.1088/1126-6708/2009/01/084
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
References in corpus (8)
- A Gravity Theory on Noncommutative Spaces
- Twisting all the way: from Classical Mechanics to Quantum Fields
- Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
- Constraints from CMB on Spacetime Noncommutativity and Causality Violation
- The Noncommutative Standard Model at O(theta^2)
- Noncommutative Geometries and Gravity
- Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
- Noncommutative Corrections to the Robertson-Walker metric