In other words, given the time/space “swapping” that occurs when crossing an event horizon, the light would be physically trapped in the singularity, but temporally moving at the time-equivalent of c?
Sounds a lot like something you’d hear in Star Trek…
And exactly the kind of thing they’d use to defeat the Borg.
Well, kinda. The speed of light is not c for all observers, light travels at the speed of c for all *inertial * observers. For a reference frame in a gravitational field to be inertial, it must be free falling. If you were freely falling into a black hole, you would observe that light travels at c. However, an inertial reference frame cannot include the singularity. To see that light does not have to travel at c, consider a photon trapped at the event horizon. It is suspended so we have light not moving at all.
We can never see the singularity. Light cannot leave the singularity so we cannot see it. Also, anything we see must be in our past light cone. The singularity of a black hole is never in our past light cone; it is always in our future light cone.
As to time and space being swapped inside the event horizon. I understand that the doomed observer’s distance from the singularity cannot increase – the distance must increase. But how does this allow the ill-fated observer to travel through time. It seems to me that his space and time axes are both time-like.