Hang on. This may get a bit weird.
Time can’t speed up more due to relativity. There’s a maximum speed in space (the speed of light), but the part where it gets really weird is that everything travels through spacetime at the same constant speed. This means you and anything not moving with respect to you is travelling through time as fast as you can go because all of your spacetime “speed” is in the time direction with none in the space directions.
As soon as things start to move or spacetime gets warped to bend paths in space (which is what gravity is) time has to slow down to allow the motion in space. The more motion there is in space, the more time slows down from the perspective of both moving things. Eventually we’d get to things going at the speed of light and they experience zero time since all their speed is in space and none is in time. That’s why photons can carry information. They don’t experience time and therefore can’t change on their way from point A to point B.
I’ll freely admit I’m not an expert, so I’m not certain if funky things like negative mass can bend spacetime to increase time flow. My understanding is that that’s impossible, but I’d be happy to hear different in a reply comment.
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