Light and Escape Velocity

The idea of light being trapped by a black hole because the escape velocity exceeds that of light is a useful one, but it can't be pushed too far. It brings to mind throwing a ball into the air, having it come to rest, and then falling back to Earth. The analogy of a ball falling back to Earth with the trapping of light in a black hole is only a crude and suggestive one that is not correct at a fundamental level. For one thing, the ball has mass, but light does not. This difference is critical, because massless particles must travel at light velocity, but massive particles cannot travel at light velocity.

Spacetime Paths Near the Black Hole

Black holes almost certainly exist, and one of their basic properties is that they trap light. However, it is also true that nothing exceeds the speed of light. In fact, the theoretical prediction of black holes is due to the general theory of relativity, which is built on the principle that the speed of light in a vacuum is constant.

You Can't Get there from Here
To understand fully why a black hole can trap light but the light still always travels at constant velocity requires an understanding of the general theory of relativity. However, the essential point is that the black hole curves spacetime back on itself. This means that all paths in the interior of the black hole lead back to the singularity at the center, no matter which direction you go (see the analogy discussed in the right frame).