Do Gravitational Waves Actually Repel Spacetime? I read something explaining that gravitational waves actually repel space-time.  It described the following.  Mass bends space-time creating gravity.  A massive object like the Sun, if it suddenly disappeared the space-time it bent would spring back up and the space it compressed (it's gravity well) would form a gravitational wave that would hit Earth sending it flying into space.  It concluded that gravitational waves squeeze and stretch space-time and actually repel it.  Is this valid?  
 A: It is correct to say that gravity bends spacetime (not just space and not just time individually). 
What do you think gravitational waves are? Nothing fancy, just gravitational fields variable in time. This is exactly the same definition one gives to 
electromagnetic waves:  EM fields variable in time
sound waves: pressure fields variable in time
water waves: sea level variable in time
So nothing special as you see.
Do they exist? 
Of course they exist! 
Really? Where? 
Just sit on the beach and look at the sea and watch the whole water content of the Earth (!!!) going up and down with the tide. If it is low tide, gravity is squeezing the water toward the bottom of the sea and at the same time, somewhere else, it is stretching water away from the bottom (and there you have high tide). 
The combined gravity of Earth, sun, moon changes in strength and direction, depending on the relative positions of these 3 celestial bodies. Of course also the other planets play some role, in principle, but in practice the effect is negligible.
How do you measure a gravitational wave? Exactly in the same way that you measure all the other waves mentioned above: you take some things sensitive to the field in question and you watch them being moved around by the wave. 
So for sound waves you put a membrane and watch it vibrating (as in your eardrum or in a microphone) , for EM waves you watch cherged particles (for ex. electrons in an antenna) moving around and thus creating a current, for water waves you put buoys and watch them moving, ect.
And for gravitational waves? Same story: take any objects sensitive to gravity (thus anything really, even your cat) and watch them moving closer or further to each other when a gravitational wave is passing. This is exactly what happens with the gravitational wave that we call tide. The whole planet (and its water) is a giant antenna. Water masses are squeezed at one place and stretched at another.
That is the idea in principle.
However when we want to measure the gravitational waves produced by changing gravitational fields of collapsing black holes 100's of light-years away, your cat is not sentitive enough.  
We place giant balls miles and miles away and try to measure ever so tiny relative displacements in their positions. 
I would not use the expression "gravitational waves repel spacetime". I'd rather say that they stretch and squeeze spacetime in a way that changes in time.
