Lorentz violation in the linearized gravity
  We study some physical consequences of the introduction of a Lorentz-violating modification term in the linearized gravity, which leads to modified dispersion relations for gravitational waves in the vacuum. We discuss two possible mechanisms for the induction of such a term in the Lagrangian. First, it is generated at the quantum level by a Lorentz-breaking coupling of the gravity field to a spinor field. Second, it appears as consequence of a particular modification of the Poisson algebra of the canonical variables, in the spirit of the so-called ``noncommutative fields approach''. 
A. F. Ferrari, M. Gomes, J. R. Nascimento, E. Passos, A. Yu. Petrov,   A. J. da Silva