Does the speed of light increase as it nears the event horizon due to the influence of a black hole’s gravitational pull?
The short answer is no, the speed of light is always the same. To explore the subtle aspects of this question, we will consider it in the context of Albert Einstein’s general theory of relativity, the simplest theory for gravity that is consistent with experimental observations. In general relativity, the familiar three spatial dimensions combine with time to make up a four-dimensional “spacetime”. Matter such as stars and galaxies can warp the geometry of spacetime so the “shortest path” connecting two points may no longer be a straight line. This is one reason that light may be affected by gravity. However, light has no mass so it is not accelerated by gravitational forces. Even when light travels on a curved path it does so at the “speed of light” which is a universal speed limit.
This is where black holes come in. A black hole is a region of space that is so warped that not even light can escape. As an example, imagine throwing a ball up in the air. Earth’s gravity will cause the ball to fall back down after a few seconds. However, if you built a machine to throw the ball fast enough (roughly 25,000 miles per hour) then it would overcome the Earth’s gravity and escape forever. Now imagine compacting the mass of the Earth into the size of a thimble. That is the point where the speed to escape becomes the speed of light. Nothing can go faster than the speed of light, so nothing can escape a black hole. If light could go faster than the “speed of light”, then it could escape the event horizon, and would no longer qualify as a black hole.