| Noncommutative Deformation of General Relativity Ivan G. Avramidi (Department of Mathematics, New Mexico Tech) ABSTRACT: We develop a novel approach to gravity that we call Matrix General Relativity (or Gravitational Chromodynamics). Gravity is described in this approach not by a Riemannian metric but by a matrix-valued symmetric 2-tensor field. We define the matrix extensions of standard constructions of differential geometry including connections and curvatures, and finally, an invariant functional of the new field that reduces to the standard Einstein action functional in the commutative case. We call the new degrees of freedom of gravity associated with the matrix structure `gravicolor' and introduce a new gauge symmetry associated with this degree of freedom. Possible phenomenological applications and open problems are discussed.
May 5, 2008 Ivan Avramidi, New Mexico Tech |