The speed of light is a constant, it does not matter in or out of a black hole.
The "boundary" you're probably thinking of is called the event horizon. Past this point, the escape velocity of the black hole exceeds the speed of light, meaning nothing, including light, can escape it.
At the point of the event horizon, the pull of gravity is so strong that the escape velocity reaches the speed of light. As such, when light reaches this point, it cannot escape.
When you are near the event horizon, you would be close to the speed of light - from your own point of view. From the point of view of an outside observer, you would move slower and slower, and never quite reach the event horizon. This has to do with the queer distortion of space and time caused by the black hole.
The distance from a simple black hole's center to the event horizon where escape velocity equals the speed of light is called the Schwarzschild radius, named after the mathematician who solved the relevant field equation from Einstein's theory of General Relativity. The distance can be calculated for a known mass using twice the product of the gravitational constant and the mass, divided by the square of the speed of light.
While nothing can escape from within the event horizon of a black hole, matter that has not yet passed that point of no return still has a chance. When a large amount of matter falls into a black hole, there is not enough room for all of it to reach the event horizon. What doesn't fall into the event horizon gets ejected in two jets of subatomic particles traveling at almost the speed of light.
That is the "point of no return". Within the event horizon, gravity is so strong that anything that crosses the event horizon can't get out, even if it moves at the speed of light.
The "boundary" you're probably thinking of is called the event horizon. Past this point, the escape velocity of the black hole exceeds the speed of light, meaning nothing, including light, can escape it.
The so-called "event horizon" of a black hole is the point-of-no-return. That means that anything that gets inside the event horizon can't get out any more, even if if it moves at the speed of light.
At the point of the event horizon, the pull of gravity is so strong that the escape velocity reaches the speed of light. As such, when light reaches this point, it cannot escape.
The word "black" aptly describes the inability of light to escape - all light and matter that passes the event horizon can only do so in one direction, falling in. The reason is, the escape velocity inside the event horizon is greater than the speed of light, the event horizon itself being the boundary at which the escape velocity is equal to that speed. Outside that horizon, the escape velocity is less than the speed of light, hence it would be possible for light and objects moving at speeds approaching that of light to escape.
By definition, the event horizon is a boundary of a black hole at which escape velocity reaches "c", the speed of light. Hence, the event horizon defines a boundary, within which, events can't affect an outside observer; neither light nor matter can escape.
When you are near the event horizon, you would be close to the speed of light - from your own point of view. From the point of view of an outside observer, you would move slower and slower, and never quite reach the event horizon. This has to do with the queer distortion of space and time caused by the black hole.
The distance from a simple black hole's center to the event horizon where escape velocity equals the speed of light is called the Schwarzschild radius, named after the mathematician who solved the relevant field equation from Einstein's theory of General Relativity. The distance can be calculated for a known mass using twice the product of the gravitational constant and the mass, divided by the square of the speed of light.
The event horizon is not a surface you can touch, or from which things can "bounce off". It is simply the point of no return - if anything gets inside the event horizon, then it can't get out anymore, no matter in what direction it moves, and even if it moves at the speed of light.
While nothing can escape from within the event horizon of a black hole, matter that has not yet passed that point of no return still has a chance. When a large amount of matter falls into a black hole, there is not enough room for all of it to reach the event horizon. What doesn't fall into the event horizon gets ejected in two jets of subatomic particles traveling at almost the speed of light.
Our mathematics and physics are incomplete; at the extremes, we do not know what will happen in areas of extreme speed or high mass. It's not so much that the "event horizon" makes things invisible, as it is that our math isn't able to describe accurately what might be going on there.
No. Nothing can escape a black one it crosses the event horizon. In most cases a black hole is in the vacuum of space, which cannot carry sound. Matter falling into a black hole will reach incredible speeds, potentially approaching the speed of light, so sound could not move though that matter, even away from the event horizon.