It seems that gravitational waves do not exist:
- Gravitational wave findings could amount to dust...
- First all-sky search for continuous gravitational waves from unknown sources in binary systems
From the theoretical viewpoint, gravitational waves are ill defined because gravitational equations are non-linear. An energy-momentum tensor of a gravitational field also is under discussion since it reduces to the boundary terms.
Moreover, it may happen that, being a Higgs field, gravitational field is not quantized, but it is classical in principle (#)