Where do gravitational field lines go exactly? We know where they start, but

Question

update/clarification: I have commented and have then been invited to include more here. I didn't say explicitly that I was not restricting physics to a simple Newtonian model, so that is now said.

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When we study electrostatics we have the pleasure of both starting and terminating electric field lines on opposite charges.

Termination behavior of gravitational field lines at one end on small volumes of mass is an instructive analogy as is attested to in both answers to Which mass distributions guarantee two bodies have non-Keplerian orbits? Which non-spherical distributions still allow noncircular Keplerian orbits?

However, the fate of the other ends of those lines is "left as an exercise for the reader" so to speak.

Question: Where do gravitational field lines go exactly? We know where they start, but if we were to follow them mathematically and/or theoretically, what would we find at the other end? Would we find the other end at all?

Answer 1

Newtonian gravity is mathematically identical to electrostatics with only one type of charge (positive or negative). Much like with a configuration of positive charges, the field lines "end" at infinity (or start there, depending on how you look at it).

Answer 2

I think the idea is quite simple here. You may be familiar with the idea of fields. So be it electromagnetism or gravity, the range of the force is ideally taken to be infinite (the field falls as 1/r^2 ). Now the field lines are just imaginary lines drawn to show the difference between positive and negative charges in case of electromagnetism (because the direction of the filed lines tell you about the nature of the charge!). In case of gravity it is better to think not in terms of field lines but in terms of the curvature of the space-time.

There is also a brilliant loophole in the idea of infinite range force in classical electromagnetism. Suppose you have a charge q sitting at earth and suddenly you introduce a charge q' in some other galaxy. Do you think the q' charge will feel the force of q immediately? But remember Einstein's Special theory of relativity says that no information can go faster than the speed of light. Then how can q' feel the force of q immediately? This is precisely one of the key arguments in QFT and there we introduce the idea of virtual particles (photons in this case) :)