D.V. Vassilevich
Diffeomorphism Covariant Star Products and Noncommutative Gravity
The paper is published: Classical Quantum Gravity 26 (2009) 145010

MSC:

81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}

83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories

PACS: 02.40.Gh,04.60.Kz
Abstract: 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.