# Will the speed of gravity and the speed of light always be the same?

I have been considering the following though experiment: If the entire sun were to disappear at once, would we feel it first due to the sudden drop in gravity or see it first? The answer I have come across is that we would feel and see it at the exact same time. I know though that light will travel slower through different medians. This means that the time it will take the light to reach us will actually be slightly greater than the distance divided by the speed of light. Will gravity also be slowed down or will we feel the effects of gravity dropping off slightly before we stop seeing the light?

General relativity can be expanded in orders of $G$ and $1/c^2$, so that the lowest order term is Newtonian gravity, the next order term gives the correction to orbits such as Mercury around the sun, and the third order term accounts for the gravi-magnetic field detected by Gravity-B probe. These first three orders, sometimes called N, PN, PPN and PPPN, for N meaning Newton and P meaning post. This is the post Newtonian expansion for gravity. The next order term gives equations that are similar to Maxwell's equations. This is the domain of linearized and weak gravitational radiation. It describes gravitational waves that move at the speed of light.