Hello, I was wondering, since gravitational waves carry energy-momentum, would it be possible to find them in regions where the components of the metric tensor vanish? That is to say, empty space (non-quantum) is described by a vanishing energy-momentum tensor - but then, if gravitational waves propagate in such regions, how can there be no energy-momentum in the region?
Hi, Certainly you didn't mean the metric tensor vanishes, you mean't [itex]\mathbf{R}=0[/itex] is satisfied, or [itex]\Box h_{\alpha\beta}=0[/itex] is satisfied. indeed the stress energy momentum tensor (SEM) [itex]T_{\alpha\beta}[/itex] is for matter. There is another SEM tensor for gravity Stress Tensor for gravity You will also want to read about the Conformal tensor, or the Weyl tensor [itex]C^{\alpha}{}_{\beta\gamma\delta}[/itex]. The Conformal tensor gives information about how much spacetime curvature is due to the gravitational field and not from matter, or how much curvature there is far from any sources. The Conformal tensor is a part of the decomposition of the Riemann curvature tensor, and is completely anti-symmetric.