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Well, the answer here is "maybe," depending on where you are.

For this discussion, a black hole has two important parts. These
are the *event horizon* and the *singularity*. The singularity is
the
center of the black hole and is a point where space and time basically
cease to exist, at least in any way that we understand. The singularity
is really the "hole," if you like, because that's where things "fall in"
and (as far as we know) completely cease to exist in our universe.
The event horizon is a surface surrounding the singularity (a sphere
in the simplest case), and represents the "point of no return" in
the sense that, once you cross it, you can't get back and are doomed
to fall into the singularity. The event horizon isn't so much an "object"
as a mathematical construction, dividing the region of space
where you could still (in principle) escape the black hole, and that
where you will inevitably fall into the singularity.

So, if I read your question correctly, you are perhaps thinking that because light cannot escape a black hole (more correctly, the region inside the event horizon), that it builds up in there. It is true that light cannot escape once it crosses the event horizon, but once this happens it simply continues on to the singularity and disappears. Of course, as you get closer to the singularity, light rays from all different directions are converging together (i.e., focusing), so in that sense it gets brighter as you approach the black hole's center.

Keep in mind that all of the above discussion is "according to the current theory." We don't really know what happens on the other side of the event horizon. We simply assume that the physics which describes gravity on one side of the event horizon also describes it on the other side, just for consistency. Similarly, the appearance of the singularity at the center of the black hole is simply the result of the application of the same theory. Because the event horizon hides what happens on the other side, physicists may propose alternate theories of what actually occurs there, with no danger of ever being proven wrong! However, these theories are more in the realm of informed speculation than science . . . .

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