Related papers: Noncommutative gravity: fuzzy sphere and others
We develop a novel approach to gravity in which gravity is described by a matrix-valued symmetric two-tensor field and construct an invariant functional that reduces to the standard Einstein-Hilbert action in the commutative limit. We also…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
We formulate a noncommutative description of topological half-flat gravity in four dimensions. BRST symmetry of this topological gravity is deformed through a twisting of the usual BRST quantization of noncommutative gauge theories. Finally…
We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable, but not conformal invariant. Questions concerning the $\b$ function and the effective action are addressed, and the effective action and the…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
We consider simple extensions of noncommutativity from flat to curved spacetime. One possibility is to have a generalization of the Moyal product with a covariantly constant noncommutative tensor $\theta^{\mu\nu}$. In this case the…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
The one-dimensional ${\cal N}\times {\cal N}$-matrix Chern-Simons action is given, for large ${\cal N}$ and for slowly varying fields, by the $(2k+1)$-dimensional Chern-Simons action $S_{CS}$, where the gauge fields in $S_{CS}$ parametrize…
We discuss the interplay between direct constraints on non-Newtonian gravity and particle-physics bounds in models with large extra dimensions. Existing and future bounds and the most effective ways of further testing these models in…
A calculation of the one loop gravitational self-energy graph in non-anticommutative quantum gravity reveals that graviton loops are damped by internal momentum dependent factors in the modified propagator and the vertex functions. The…
We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make…
In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3) group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
A review is made of recent efforts to find relations between the commutation relations which define a noncommutative geometry and the gravitational field which remains as a shadow in the commutative limit.
We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only. We found various kinds of nontrivial solutions, by applying a similar technique which was used to seek…
We investigate gravitational radiation in dynamical noncommutative spaces. By including corrections to the gravitational potential due to dynamical noncommutativity, we calculate the power in gravitational radiation and use observational…
The quantum gravity problem of N point particles interacting with the gravitational field in 2+1 dimensions is approached working out the phase-space functional integral. The maximally slicing gauge is adopted for a non compact open…
We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge fields as well as additional scalar fields…
Two families of noncommutative extensions are given of a general space-time metric with spherical symmetry, both based on the matrix truncation of the functions on the sphere of symmetry. The first family uses the truncation to foliate…