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Diffeomorphism covariant star products and noncommutative gravity

D V Vassilevich

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The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of all two-dimensional dilaton gravity models thus overcoming some difficulties of earlier approaches. One of such models appears to be integrable. We find all classical solutions of this model and discuss their properties.


PACS

04.50.-h Higher-dimensional gravity and other theories of gravity

02.40.Pc General topology

02.40.Gh Noncommutative geometry

02.40.Sf Manifolds and cell complexes

MSC

58B34 Noncommutative geometry (à la Connes)

83C65 Methods of noncommutative geometry (See also 58B34)

53D55 Deformation quantization, star products

57R50 Diffeomorphisms

58D05 Groups of diffeomorphisms and homeomorphisms as manifolds (See also 22E65, 57S05)

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 14 (21 July 2009)

Received 26 April 2009, in final form 25 May 2009

Published 25 June 2009



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