Non-commutative Corrections in Spectral Matrix Gravity
  We study a non-commutative deformation of general relativity based on spectral invariants of a partial differential operator acting on sections of a vector bundle over a smooth manifold. We compute the first non-commutative corrections to Einstein equations in the weak deformation limit and analyze the spectrum of the theory. Related topics are discussed as well. 
Guglielmo Fucci and Ivan G. Avramidi