Chern-Simons formulation of noncommutative gravity in three dimensions

Abstract

We formulate noncommutative three-dimensional (3d) gravity by making use of its connection with 3d Chern-Simons theory. In the Euclidean sector, we consider the particular example of topology T 2 × R and show that the 3d black hole solves the noncommutative equations. We then consider the black hole on a constant U(1) background and show that the black hole charges (mass and angular momentum) are modified by the presence of this background. * CONICET † Associated with CICBA

Noncommutative Bianchi Type II Quantum Cosmology

“…In particular, Compean et al, (Compean et al,2002(Compean et al, ,2003a avoid the difficult technicalities of analyzing noncommutative cosmological models, when these are derived from the full noncommutative theory of gravity, see by example (Bañados et al, 2001;Nishino-Rajpoot,2002;,hep-th/0203038; Abe-Nair,hep-th/0212270; Cardella-Zanon,hep-th/0212071; Chaichian et al, 2001), their proposal is to introduce the effects of noncommutativity in quantum cosmology including one θ parameter, deforming the minisuperspace. This deformation is achieved through a Moyal deformation of the Wheeler-DeWitt (WDW) equation, this is similar to noncommutative quantum mechanics (Gamboa, 2001;Chaichian et al, 2001).…”

Noncommutative Quantum Cosmology

“…In particular in reference [13] a deformed Einstein gravity is constructed by using the Seiberg-Witten map [9], gauging the noncommutative ISO(3,1) group. Some aspects of noncommutative 2 + 1-dimensional Chern-Simons gravity have been also studied [14,15].One of the puzzles in quantum gravity is the measurement of length, which seems to be limited to distances greater than the Planck length L P , because to locate a particle we would need an energy greater than the Planck mass M P . The corresponding gravitational field will have an horizon given by the Schwarzschild radius R = 2GMP c 2 = 2L P and, whatever happens inside, this radius is shielded and therefore a minimal size should exist for quanta of space and time configuration.…”

Noncommutative topological theories of gravity

“…(12). The result is given by a rather long expression, which however is proportional to the unity matrix 1, like (33).…”

“…However, as pointed out in these works, [9,10], they could be made diffeomorphism invariant, substituting the Moyal * M -product by the Kontsevich * Kproduct. For other recent proposals of noncommutative gravity, see [11,12,13,14,15,16].…”