The flight of the bumblebee: solutions from a vector-induced spontaneous   Lorentz symmetry breaking model
  The vacuum solutions arising from a spontaneous breaking of Lorentz symmetry due to the acquisition of a vacuum expectation value by a vector field are derived. These include the purely radial Lorentz symmetry breaking (LSB), radial/temporal LSB and axial/temporal LSB scenarios. It is found that the purely radial LSB case gives rise to new black hole solutions. Whenever possible, Parametrized Post-Newtonian (PPN) parameters are computed and compared to observational bounds, in order to constrain the Lorentz symmetry breaking scale. 
Orfeu Bertolami and Jorge Paramos