Can GWs move objects (excerpt pressure on matter) like EM waves? Gravitational waves are real, they have been observed.


Gravitational waves are disturbances in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light.


https://en.wikipedia.org/wiki/Gravitational_wave
There is no consensus whether these GWs' quanta are the hypothetical gravitons or not.
But we do know that EM waves can excerpt pressure on objects. This is how the solar sail works.


Solar sails (also called light sails or photon sails) are a proposed method of spacecraft propulsion using radiation pressure exerted by sunlight on large mirrors. 
    But Solar radiation exerts a pressure on the sail due to reflection and a small fraction that is absorbed


https://en.wikipedia.org/wiki/Solar_sail
We know that photons do excerpt pressure on matter they interact with.


Yes. Actually photons exert pressure on any surfaces exposed to them. For example, photons emitted by the Sun exert pressure of 9.08μN/m2 on the Earth.


About photons and mirrors


Radiation pressure is the pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength which is absorbed, reflected, or otherwise emitted (e.g. black-body radiation) by matter on any scale (from macroscopic objects to dust particles to gas molecules).


So radiation pressure can move objects.


Radiation pressure can equally well be accounted for by considering the momentum of a classical electromagnetic field or in terms of the momenta of photons, particles of light. The interaction of electromagnetic waves or photons with matter may involve an exchange of momentum. Due to the law of conservation of momentum, any change in the total momentum of the waves or photons must involve an equal and opposite change in the momentum of the matter it interacted with (Newton's third law of motion), as is illustrated in the accompanying figure for the case of light being perfectly reflected by a surface. This transfer of momentum is the general explanation for what we term radiation pressure.


So basically both classicall EM waves and QM photons do excerpt pressure on the matter they interact with, and this is due to conservation of momentum.
Now since GWs are waves too, and there are similarities between them and EM waves, even if we treat GWs classically or in QM as made up of gravitons, GWs should excerpt pressure on matter they interact with.


Due to the weakness of the coupling of gravity to matter, gravitational waves experience very little absorption or scattering, even as they travel over astronomical distances. In particular, gravitational waves are expected to be unaffected by the opacity of the very early universe.


Now the difference between EM and GWs is that basically GWs weakly couple to matter.
Question:


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*Can GWs move objects (excerpt pressure on matter)?

 A: Yes they can exert pressure similarly to EM waves, but it is a bit more subtle and I haven't seen it discussed in textbooks so perhaps someone more expert than me can comment.
One way to see that EM waves exert a pressure is to calculate something called the energy momentum tensor. This is a matrix that tells you (among other things) the energy and momentum density of the electromagnetic field. The momentum densities turn out to be given by the Poynting vector which is how the idea of radiation pressure is usually introduced in introductory physics textbooks.
Now for gravitational waves there are conceptual issues defining the energy momentum tensor. You can read about these difficulties if you search about problems defining the energy of the gravitational field. But in practice there are standard ways to define the energy momentum tensor which work well enough. So you can find the momentum density of gravitational waves just like for electromagnetic waves.
Another more direct way to see radiation pressure is to imagine how a test particle behaves when a transverse EM wave passes by. The electric component makes the particle want to move transverse to the wave direction, but then the secondary effect due to the presence of the magnetic field pushes it in the radiation pressure direction.
In gravity some of the same approximations that allow us to define an energy momentum tensor lead to an approximation called gravitomagnetism, where you can define something like a magnetic field for gravity. In textbooks only the transverse motion of test particles is discussed, but I am almost certain that if the higher order gravitomagnetic effect is considered you would see the test particle move in the radiation pressure direction (but perhaps an expert or someone who wants to do the calculation can verify).
