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How does gravitational time dilation affect the transmission of mechanical forces in a hypothetical scenario where a tether extends from a less gravitationally influenced region, like the edge of the solar system, into a stronger gravitational field, such as near a black hole? Specifically, does general relativity predict any modification in the force perceived at the far end due to time dilation effects?

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Not sure time dilation is that important here. Basically, you want to be working with covariant quantities, such as four-momentum. Time-dilation will be taken care of automatically. Now to the mechanical force. Since there are some serious limitations around things not accelerating past the speed of light, you will not be able to simply hand-wave and say 'mechanical force'. You will need to specify constitutive equations, i.e. how much energy will need to be spent to extend the material by a certain distance. You can talk about force, but it should probably be four-force.

So perhaps a better way to approach this question would be to ask how constitutive equations should be written in special/general relativity. I am not familiar with this literature, but I could probably hazard a guess about the correct form of the tensorial equation that describes relationship between four-force and deformation of the tether. The short summary would be though that you will not have a fixed length tether anymore - it will be more like an elastic spring. And if the spring is elastic, then there will be a gradient of force along it as soon as you try to accelerate it, so placing such tether into gravitational well will lead to different tension along the length of the tether

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  • $\begingroup$ This is an excellent response, I'll do some more research on this. Thank you! $\endgroup$
    – Travis R
    Commented Apr 28 at 19:33

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