To demonstrate that the speed of gravity is no faster than light, physicists love to point out that if the sun suddenly vanished, it would take approximately eight minutes for the information to reach earth, and over five hours for the information to reach Pluto. It is assumed that earth and Pluto would remain under the influence of the sun's gravity for eight minutes or over five hours respectively. After all, it is currently understood that information, including gravitational information cannot exceed light speed.
But here is the irony: to make the point that nothing is faster than light, the sun (poof!) disappears faster than light! Further, such a thought experiment only takes into account an observer on earth (or Pluto). Allegedly, both gravitational and electromagnetic information reach the observer simultaneously, so said observer (Alice) observes nothing out of the ordinary. She sees the sun vanish and notices that the sun's gravity has vanished along with it. However, another observer (Bob) has parked his spaceship telescope halfway between the sun and the orb where Alice is located (see drawing below).
The orb is distance r from the sun and Bob's telescope is distance r from the sun and the orb. Information from the sun and the orb reach Bob simultaneously within a time of r/c seconds, where c is light speed. Now, let's suspend disbelief and pretend the sun vanishes instantaneously (see drawing below).
Because information from the sun and the orb reach Bob simultaneously, Bob must wait another r/c seconds to observe what Alice observes. Suppose he doesn't wait. Suppose he plugs in the numbers he observes when he first receives information from the sun and the orb. Here is what Bob's math reveals:
At 1) we have Einstein's field equation. If the sun vanishes, the stress-energy tensor (T) value would be severely reduced, so at 2) T has a limit of zero. A little algebra gives us a value that is substantially greater than the gravitational constant. Both 2) and 3) reveal that Newton's constant is not constant, i.e., has a much greater value than expected for a time period of r/c, the time it takes for the information to reach Alice.
If we assume that gravitational information is necessary and that it propagates at light speed, then we must abandon the idea that Newton's constant is constant for all observers. Clearly it is not if gravitational information is necessary to cause gravity.
On the other hand, if we assume gravity is more analogous with the equivalence-principal thought experiment, where the dropped pen seems to fall to the spaceship's floor but the floor really accelerates to the pen, then gravitational information is not necessary to cause gravity. Further, the math shows that Newton's constant remains constant, because there is no r/c time delay--the spaceship does not send a signal to the pen--it simply accelerates to the pen, creating the "persistent illusion" of gravity, where reality, according to Einstein, is a "persistent illusion."
Of course nothing I have written here addresses gravitational waves or how gravity is supposed to work outside an equivalence-principle spaceship. I address those concerns in "The Beautiful Destruction of the Graviton" and "Quantizing Gravity without the Graviton."--which you can find at my profile page at Accademia.edu.
OK, then ... if the sun should magically disappear what really happens? If Newton's constant is really a constant, the impact on the solar system will be immediate but this will not violate the light-speed limit because no gravitational information needs to propagate from the sun.
