If I treat you as if you are in third grade then I apologize. That's why I asked "are you talking about special relativity?". In any case, we first repeat the basics and then move on from there.
***What you, and a whole lot of people, don't understand, is that the phrase "movement along the t axis" does not make any sense at all. It's as meaningless as the question "when did time begin". Just as time cannot "begin", for beginning is an action and actions happen in time, you cannot "move through time" as movement already implies the concept of time. The reason you can't "move through time" at any "speed" different than one second per second is the same reason why you can't move through space at a distance less than one meter per meter. It doesn't make any sense and reference frames have nothing to do with it, other than the fact that they cloud your mind and prevents you from seeing what's ultimately a trivial truth.***
Aurino, I think we need to differentiate special relativity (SR) from general relativity (GR). In SR the concept of Riemannian geometry and curved space and curved time was not developed. So, there is no issue about moving through time along a fixed dimension. It is all about reference frames.
In GR, the issue of (x,y,z,t) and curved spacetime is the focus. My understanding is that gravity is treated as part of a gravitational field that actually composes spacetime. Philosophically, I believe, Einstein was an eternalist. Meaning, that we are simply located in a particular region of spacetime. When we 'move' through space, or when we 'move' through time, we are not actually moving in a second by second basis, rather we are already 'there' in the future. In a sense, the passage of time is an illusion.
This picture, though, is not consistent with quantum mechanics since the uncertainty principle prohibits some of the features of this static eternal universe.
Warm regards, Harv