I Why do gravitational waves travel at the speed of light?

[brucegoth123]

Why are gravitational waves able to move at the speed of light?

 

[Ibix]

Within general relativity the answer is just that the Einstein field equations admit a wave solution that has the speed of light.

We don't have a working quantum theory of gravity, but we expect that the graviton will be massless and hence gravitational waves propagate at the speed of light because that's what massless things do.

Does that help?

 

[PeroK]

Why are gravitational waves able to move at the speed of light?

It's a good question without a simple answer. We can look at it as follows:

Spacetime has a universal constant, which we call $c$, which determines the relationship between space and time. It's really just a conversion of units from spatial distances to units of time. If we measure distance in metres and time in seconds then $c \approx 3 \times 10^8 m/s$.

Because light is massless electromagnetic radiation, this radiation must move at this specific speed $c$. This is shown by both SR (light as a massless particle) and Maxwell's equations of electromagnetism. And, of course, the historical development of relativity began with the experimental evidence that light propagates at this invariant speed. Hence $c$ is "the speed of light". A more modern view is that $c$ is determined by the geometry of spacetime and light must move at that speed.

Now, the equations governing GR also have this universal constant at their heart; and, for similar reasons, the effects of gravity (including gravitational waves) must propagate at this invariant speed $c$.

In that sense, it's not such a coincidence. It's that the propagation of light at gravity are both determined by the fundamental geometry of spacetime, and share the same universal invariant speed $c$.