What happens to time when speed increases approaching the speed of light?
Time is geometry. It is a dimension and there may be more than one temporal dimension (Vafa, Wesson).
Time is relative to space such that, for instance, while a week passes in the vicinity of a black hole simultaneously 40 years may pass on earth.
And if you were to travel through space at a constant acceleration of one earth gravity, while 25.3 years elapsed on your voyage, 5x1010 years would elapse on earth.
And, ta da, 6 equivalent days at the inception space/time coordinates of this universe are equal to approximately 15 billion years from our space/time coordinates. (Inflationary Theory and Relativity)
Special relativity looks at space/time as a cube, general relativity on the other hand looks at the fabric of space/time as warped, curved space.
Massive (high positive gravity) objects are indentations in space/time. Thus an object must achieve escape velocity to get out of the indentation, and the paths of objects approaching nearby will be bent by the indentations. Even light bends.
The equivalence principle derives from the Newtonian notion that all objects fall with the same acceleration and thus how fast an object accelerates (inertial mass) and gravitational mass are the same. Thus falling towards gravity, indentations in of space/time (general relativity) and velocity are equivalent. In the strong version, even gravitational “self-energy” must follow the same rule.