Symmetry reduction in twisted noncommutative gravity with applications to cosmology and black holes

Thorsten Ohl; Alexander Schenkel

doi:10.1088/1126-6708/2009/01/084

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Symmetry reduction in twisted noncommutative gravity with applications to cosmology and black holes

Thorsten Ohl and Alexander Schenkel

Published 30 January 2009 • Journal of High Energy Physics, Volume 2009, JHEP01(2009)

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Author e-mails

ohl@physik.uni-wuerzburg.de

Author affiliations

Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany

Dates

Received 28 October 2008
Accepted 9 January 2009
Published 30 January 2009

Citation

Thorsten Ohl and Alexander Schenkel JHEP01(2009)084

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DOI

https://doi.org/10.1088/1126-6708/2009/01/084

E-print

http://arxiv.org/abs/0810.4885

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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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