Testing local Lorentz invariance with gravitational waves
  The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation. 
Alan Kostelecky and Matthew Mewes
gr-qc astro-ph.HE hep-ph