Question

Do gravitational waves have field components like electromagnetic waves?

Answer 1

This is entirely natural, of course, asboth are relativistic theories. It is perhaps for gravitational waves that the links between the two are most readily apparent. In the absence of matter, both electromagnetic andgravitational waves are transverse and propagate at the speed of light.

Answer 2

No.
Gravitational waves are actually ripple in the curvature of spacetime that are generated in certain gravitational interactions and propagate as waves outward from their source at the speed of light. Wecan't say they have dual nature like electromagnetic waves. So that's why gravitational waves dosent have field components like electromagnetic wave.