According to what I've read on special relativity, $c$ is the speed limit for every object in the universe, and according to Einstein, an object's speed through the three spatial dimensions plus its speed through the fourth temporal dimension always sums to $c$.
I once watched a video demonstrating what it would be like to fall into a black hole. At one point the author stated that if a photon was emitted directly away from the singularity and at a distance equal to the Schwarzschild radius, the photon would hover there for eternity.
My question is based on these assumptions so please let me know if either is incorrect.
With its motion through the spatial dimensions halted, will the photon in question not experience time at roughly the same rate we do? Will it decay?