# Visualising Gravitational waves

I'm studying General relativity, and I want to clarify the qualitative nature of how gravitational waves propagate.

Simple is best, so I want to imagine a single binary black hole system orbiting in the $x,y$ plane at $(0,0,0)$ forever at the same radius.

$$\overline h_{ij}(\mathbf x,t) = \frac{2G}{|\mathbf x|c^6}\partial_t^2\int y^iy^jT_{00}(\mathbf y, t_r) d^3y$$

$$t_r := t - |\mathbf x|/c$$

$$\overline h_{\mu \nu} := h_{\mu \nu} - \eta_{\mu \nu}\eta^{\sigma \tau}h_{\sigma \tau}$$

tells us that anywhere in space, we have the same perturbation of the Minkowski metric $h_{\mu\nu}$, just scaled by $\frac1{|\mathbf x|}$ and appropriately delayed.

I imagine this situation like the binary system is a small particle oscillating in a block of jelly (gelatin dessert, not jam) with the whole block wobbling in the same plane, and the wobbling diminishing asymptotically.

Where I start to doubt this visualisation though, is when I here that gravitational waves are transverse. Specifically, it seems like gravitational radiation is propagating in the $x$ direction, which conflicts in my head with the fact that the metric is perturbed in this direction.

Is my picture of gravitational waves in some sense accurate? What does it mean to say that gravitational waves are transverse?

Edit: This animation seems to me to conclude that the image I have in my head is wrong, namely, it has a perturbation of the metric in the $z$ direction. I simply cannot reconcile this with the quadrupole formula, which gives no perturbation in the $z$ direction.

• Commented Apr 11, 2018 at 10:42
• Hi Yuzuriha, I'm familiar with the diagram given in that answer, which shows distortion when the gravitational wave is passing through the screen. The diagram describes what someone on the $z$ axis would experience. My interpretation is that this would be true (according to the quadrupole formula) for observers on the x axis looking in the $z$ direction. so although I'm convinced the distortion is transverse in the $z$ direction, it doesn't seem so in any other direction. Commented Apr 11, 2018 at 10:58

• Isn't is true that gravitational waves travel in the x-direction as well? I know that they are travelling in the z direction if you stand on the z axis, but if you stand on the x-axis, as far as I can see, either you feel no gravitational effects, or there is gravitational radiation travelling *in the x direction*(by symmetry, it seems there is no other way they would be travelling). Such direction of travel, plus the fact that GWs are transverse demands a perturbation of the metric in the $z$-direction, no? Commented May 1, 2018 at 9:00