Effective metric in nonlinear scalar field theories
  We discuss several features of the propagation of perturbations in nonlinear scalar field theories using the effective metric. It is shown that the effective metric can be classified according to whether the gradient of the scalar field is timelike, null, or spacelike, and this classification is illustrated with two examples. We shall also show that different signatures for the effective metric are allowed. 
E. Goulart, Santiago Esteban Perez Bergliaffa
gr-qc