Speed of light in a black hole

[rcgldr]

What happens if a beam (or component) of light originating from within a black hole, is moving directly away from the center of the black hole?

 

[pervect]

The short answer is that the light moving "away" from the black hole still falls into the central singularity, it just arrives there later than the light moving "towards" the singularity.

The issue of "later" vs "earlier" is obscured in the case of black holes by coordinates - the Schwarzschild 'r' coordinate is actually a time coordinate inside the event horizon and not a space coordinate as one would think from its label.

In my earlier remark, "Later" vs "earlier" can best be understood in terms of causality. A cause must always occur "earlier" than its effect, at least as long as one doesn't have time machines. It is in the causal sense that the "outgoing" light beam reaches the singularity "after" the ingoing one.

To further confuse the issue, time machines or violations of global causality ARE possible in GR, but fortunately they don't occur in something as "simple" as a static Schwarzschild black hole.