The four-vector contains coordinates of a point in time and space (x,y,z,t).

As a sibling said, light travels forward in time, but also from a light source towards the camera. Raytracing traces rays backwards from the camera (because there are fewer rays to trace this way: just pick the ones that land on the camera and work backwards towards light sources). So backwards in time, trying to figure where the ray originally came from.

Anyway, you need to keep track of the time dimension as light moves (at constant speed) through spacetime in a straight line, but the black hole also stretches the time dimension, affecting what a straight line looks like for an outside observer.

That's my understanding at least, I am not that well versed in relativity.

Edit to make it more interesting: (x, y, z, t) is your position in spacetime, I do not quite understand how you can take its derivative¹ (probably not time-wise), but you can derive the four-velocity, the magnitude of which is constant (c). Intuitively (and probably naïvely) I understand this as: you move trough spacetime at constant speed. Therefore, if your spatial coordinates move faster, your time coordinate moves slower. This gives you back the special relativity results with time that "slows down" for fast-moving objects.

https://en.wikipedia.org/wiki/Four-vector

https://en.wikipedia.org/wiki/Four-velocity

¹: derivated along the "proper time" (time from the perspective of the moving object) according to Wikipedia. Still unsure how to compute that.

Can you clarify your question? Light does not travel in time -- that's sort of the main characteristic of things traveling at the speed of light.