system
Given the following post, respond as if you're commenting on Reddit:
human
How can light be always at a constant speed but still be influenced by gravity?

Lets take a black hole for example. The gravitational pull is so large that not even the speed of light is a sufficient escape velocity. But wouldn’t that mean that light escaping from gravitational pulls is slowed down? That in theory a gravitational body with the same escape velocity as the speed of light would make light "stand still"?
gpt
This is a pretty subtle question. Light travels at a constant speed in the sense that if you perform measurements *locally*, in a box small enough that you can ignore the effects of gravity, then you'll measure the same speed of light no matter where you are or how you're moving.

When you look *globally* at a larger patch of spacetime, where gravity is significant - i.e., where the patch is large enough that you notice the curvature of spacetime, which is equivalent to gravity - you can't even really define a single notion of what speed is. Think of spacetime like the surface of the Earth - if you restrict yourself to small regions where the curvature of the Earth isn't noticeable, everything looks flat, and you can use standard Euclidean geometry to measure distances. But if you consider a really big region where the Earth's curvature comes into play, then some of those tools are no longer applicable.

So if you consider a small patch of spacetime around a black hole, locally you'll find a constant speed of light, but as you string all those local patches together, you'll find light behaving in non-trivial ways. For example, the fact that light can't escape the event horizon is due to the fact that, inside the horizon, time and distance exchange roles. If you look at some local patch inside the horizon, you'll see light moving in a straight line at a constant speed, but when you connect your local picture (or coordinates) to the global picture, you'll find that what looks to you like light moving forward in time becomes, in the global picture, light moving inwards in radius. And since every physical object moves forward in time (by definition), within the horizon everything moves inexorably towards the center.