Suppose two parties $A$ and $B$, some distance apart and at rest relative to each other both had control of one massive local object each.
If party $A$ lifted their local object upward relative to $B$, then the total force of gravity on $B$'s mass would angle upwards slightly.
If B then measured this shift in gravitational pull over time a communication wave could be formed between $A$ and $B$.
Wouldn't this communication channel operate instantaneously? How does this not violate the laws of causality with respect to the speed of light?
Answer
Alas, no, the communication would not be instantaneous. This is a valiant attempt, and it's been considered by many people before, since we're mostly all taught Newtonian gravity before we're taught about the speed of light, and the former is then never treated again prior to general relativity.
What happens is the shift in the mass of A causes a disturbance in spacetime (a small perturbation to the background metric) and this disturbance travels outward at a speed no greater than $c$. It's exactly the same as if you moved a charge collection and had someone far away with an electromagnetic receiver (well the GR equations are nonlinear and complicated, but the same principle is at work).
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