No, they don't. Read what I said carefully. I did not say gravitational waves do not carry "energy". I said they do not have any "stress-energy". In other words, they are vacuum solutions of the Einstein Field Equation--their stress-energy tensor is zero. That is a true statement, and I contrasted it with EM waves, whose stress-energy tensor is not zero.
> It's just not localized
This is a consequence of the fact that their stress-energy tensor is zero, so there is no tensor that describes "energy carried by gravitational waves".
No, they don't. Read what I said carefully. I did not say gravitational waves do not carry "energy". I said they do not have any "stress-energy". In other words, they are vacuum solutions of the Einstein Field Equation--their stress-energy tensor is zero. That is a true statement, and I contrasted it with EM waves, whose stress-energy tensor is not zero.
> It's just not localized
This is a consequence of the fact that their stress-energy tensor is zero, so there is no tensor that describes "energy carried by gravitational waves".