Monday, 18 February 2019

general relativity - Would there be time dilation at the point where two gravitational fields cancel each other out?


My question is very simple, and most likely a stupid one:


One observer is at a point in space were the gravitational force form massive bodies (or a single massive body) cancel each-other out. The second observer is in another hypothetical situation where there exists no massive bodies and therefore no gravity. My question is this, is there a relativistic time difference between the two?



Answer



In the "weak field limit" where the graviational forces are small (such as anything in the solar system, and basically anything not right next to a black hole), the time dilation relative to a distant observer is:



$\Delta T/\Delta T_0 = 1 - \Phi/c^2$.


here $\Delta T_0$ is the time elapsed for an observer at infinity, $\Delta T$ is that time elapsed at some point in the system, and $\Phi$ is the gravitational potential at that point. As @leftaroundabout stated correctly the important factor is the gravitational potential not gravitational forces. Since potentials add, instead of cancelling like the forces, we get twice the time dilation with two planets than we get with one, as @Jim Graber said.


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