Researching, I found that gravitational waves are generated by the changing in time of the quadrupole moment of mass of a system - source. They travel at speed of light, and they perturbate the spacetime where they are. But the spacetime is statically deformed when a mass is present in it, even if the mass has not a time-varying quadrupole moment.
These characteristics are very similar to that of an electric field which can be static if in presence of a non-moving charged particle and has perturbations whenever a charge is accelerated.
Can spacetime be thought as a field exerted by mass and perturbated by gravitons?