Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 019, 15 pages      arXiv:0912.3021
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Emergent Abelian Gauge Fields from Noncommutative Gravity

Allen Stern
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Al 35487, USA

Received December 30, 2009, in final form February 14, 2010; Published online February 18, 2010

We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.

Key words: noncommutative gravity; Groenewold-Moyal star; exact solutions.

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