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Does the axis of Time point into a black hole or away from?

Can you give a reference paper?

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I'm not sure what the question means. The words "into" and "away from" have to do with space, not time. Suppose someone asked you whether next Thursday points towards or away from Chicago. What would you answer? In addition, and perhaps more importantly, there's not a unique "axis of time" -- different observers, in different reference frames and at different locations, will have different notions of the axis of time. –  Ted Bunn Jul 21 '11 at 17:42
    
Event horizon is just a boundary inside that any timelike direction points inside and so it is not possible to escape along any "axis of time". It is not possible to write a metric in diagonal form on the event horizon and it is neccesarry to use something like Eddington-Finkelstein coordinates. –  Alex 'qubeat' Jul 22 '11 at 15:44
    
There can be different interpretations, so for instance a Schwarzschild black hole has a different meaning for time (the time axis isn't uniquely defined in GR, everything is relative as mentioned below) and then for an AdS blackhole we doen't even have a notion of time. I believe the same applies to Kerr as well. Another point (already mentioned) is that a lot of what GR captures is in terms of light cones –  dhillonv10 Aug 15 '11 at 1:32
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2 Answers

There is no uniquely defined time axis is relativity. Locally, observers in different states of motion have time axes that don't coincide. Even if we fix a state of motion for the observer, there is both a forward and a backward time axis. A more meaningful question would be phrased in terms of the past and future light cones: http://en.wikipedia.org/wiki/Light_cone

In the following, I'll assume a spacetime containing a black hole that is the result of gravitational collapse. (There are other possibilities. See http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/black_holes_picture/index.html )

For any spacetime event that is inside the event horizon, we have a future light cone and a past light cone. One of these contains world-lines that all terminate at the singularity. The other contains world-lines that extend out through the event horizon. Conventionally, we call the former direction the future and the latter the past direction. (If we were to reverse these labels, then this would be a white hole, not a black hole.)

For any spacetime event that is outside the event horizon, the past light-cone (assuming the conventional labels) contains world-lines that stretch back in time but never intersect the event horizon. The future light-cone contains some world-lines that pass in through the horizon and some that don't.

The short answer to your question, phrased in the language you used, is basically that if you're inside the horizon, all possible future time axes point toward the singularity.

As far as references, you could look at any textbook on GR. If you can post more about your level of math and physics background, we could point you to something specific that would be appropriate.

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+1: good answer –  troyaner Aug 15 '11 at 6:15
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Time axis is not bent by the black hole - the light-like axis is. here we have the Eddington-Finkelstein coordinates:

Eddington- Finkelstein coordinates

Schwarzschildradius is at $r_S$ and you can see the both light-like rays, one of which is parallel to time axis, the other points towards the singularity.

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