First I must specify I am a math major and not currently taking any classes on physics and this is a casual interest/hobby of mine. Therefore I apologize in advance if my questions seem naive.
An object sits near a gravitational well. The object begins to accelerate toward the center of the gravity well. There exists a reference frame outside which sees this object falling in. The object itself is said to experience time at a slower rate as the gravity increases.
Query: Does the object experience time slower itself or is the time dilation only measurable and therefore visible to an outside reference frame but not known to the object experiencing said dilation? i.e., it's life expectancy is some arbitrary time and it lives that time according to it's own clock but to an outside observer it lives much longer.
Now let us state this object, call it particle A, is moving at 99.999% of c.
It is being followed by the outside reference frame at the same speed from a separate entity.
Call these, two particles: Particle A: the one which will intersect a black hole or some sufficiently large gravity well, and Particle B travels at the same velocity parallel to particle A but far enough away that it can observe particle A's interaction with the gravity well without being a part of the gravitational interaction.
Query: Let us assume for a moment that an object can actually reach the limit of the speed of light for it's velocity. Particle A is said to to be moving so close to C that a sufficiently large gravitational well should give it the boost necessary to reach that limit as it falls in or approaches. Since Particle A should be experiencing time at a slower rate. What does particle B see in this scenario without worrying about the particles frame slowing down, etc.?
The first question is of the most importance to myself.
-Thank you for your help.