# How fast can and do gravitational waves travel?

I was thrilled by the recent announcement of the detection of gravitational waves. The media has done a great job explaining them and the theory behind them and I get the concept fairly well.

But if it's a warping of spacetime, not a particle phenomenon, (or is it somehow?) How fast do these waves travel through space? Is it constant or variable? Slower than the speed of light or even faster? If spacetime has no resistance per se, the what would keep them from traveling infinitely fast?

I'd love to understand it better and hope my question makes sense.

## 3 Answers

Gravitational waves travel at the same speed as the speed of light in a vacuum, in general relativity. In special relativity, this is the maximum speed for any interaction in nature.

• If gravity was faster than the speed of light, then predictions we make according to the bending of light would be incorrect.

• If gravity was faster than the speed of light, then the orbits and positions of the planets would be completely different.

Those are my two main points, to help me prove to you that gravity travels at the speed of light.

Also, light is not the only thing in the universe which travels at the speed of light. It is about all massless particles! Photons and gluons are two good examples I can think of of massless particles, I'm not sure about gravitons though - but I'll still include them.

• Well gravitons are not proved so I would not talk about them much. But yes, gravity "travels" at the speed of light – Vojta Klimes Feb 18 '16 at 12:18
• Gravitational waves travel at the speed of light. – ProfRob Feb 20 '16 at 18:54
• @DanielCann Unfortunately both your points are more about static gravitational fields rather than gravitational waves – John Davis Feb 20 '16 at 20:04
• Yes - after re-reading my question I can definitely see that I haven't addressed the exact question that was asked. I think I helped contribute though. – Featherball Feb 20 '16 at 21:17

As others have said, in General Relativity gravitational waves travel at the speed of light. However, with the observation of GW170817, a gravitational wave signal from the merger of two neutron stars, coincident with a gamma-ray burst (GRB170817A), we can now set stringent limits on the difference between the speed of photons and gravitational waves. The gravitational wave signal recorded the merger time at approximately 1.7 seconds before the arrival of the gamma-rays, and the source was in a galaxy approximately 40 Mpc away, so (using 1.7 seconds as an upper limit on the time difference, and a lower limit on the distance of 26 Mpc from the uncertainty on the distance measurement) an upper limit on the difference in speeds is $\lesssim 10^{-15}$ (see Abbott et al, Ap. J. Lett. 848, 2, (2017) for details).

The most basic reason that gravitational waves travel at the speed of light can be reduced to that in the far-field (i.e. far away from the source), their speed should be independent of their source. If you like the only speed at which waves can travel through a vacuum is at the speed of light because it is the only invariant speed in a vacuum.

You are right though in that gravitational waves in general relativity are not particles or any other kind of matter but part of the spacetime metric. The way this is tackled is to take the metric $g$ and decompose it in to a background metric $g'$ and a perturbation $h$ such that $g = g'+h$. It is usual for the background metric to be the flat Minkowski metric and the speed of gravitational waves is the propagation speed of $h$ in $g'$.