A few years ago, I saw a proposal for multiplayer games which suggested that the time passage between ticks vary depending on how many users are playing within a close space, to help deal with the increased network load. This is something that Eve Online does, but it segments its game-space into discrete sectors and therefore it slows down time uniformly in these sectors. This proposal was to do the same, but variably within one contiguous gamespace, meaning players would observe each other “slowing down.”
This seemed interesting to me because, well, what on earth would it do to your game physics to have varying time passage between ticks depending on your position in space? So I rigged up a simple simulation of 2 points connected by a spring force (a “body”), gave them an initial velocity, and set the tick to slow down linearly according to distance from a “center.”
The end result was that the body orbited around the center. The varying time passage meant that the spring force’s effect on the point masses would be reduced for the points in the slower tick speed. So it seems like you can create a kind of “gravity” by bending time but not space.
Here’s a link to the sim: https://pfrazee.github.io/gsim/