# What can an observer see during his travel into BH?

1. Dec 27, 2005

### wangyi

Hi, i am confused by the following question:
When an observer is going towards the horizon of a BH from outside, he finds the light from far away so blue shifted that the far future of the far away world presents in front of him. Does that mean when he is crossing the horizon, he has seen everything in the infinite future?
If it's true, there are questions:
1. Does this break the causal principle? As the observer has got information of the whole universe, including information outside his particle horizon.
2. When he has droped into the BH, what can he see? As he has seen everything before he drops into the BH, and what he sees after he goes cross the horizon seems to be at time "after" infinity.

Thank you!

2. Dec 27, 2005

### pervect

Staff Emeritus
What makes you think this?

To actually calculate the path of the light is somewhat involved, the only way I can think of to do it would be to do a ray trace.

The only website I've seen that talks about this topic has some nice graphics, but doesn't go into the detail of how the calculations were performed.

(This site has several movies, note that only one of the later movies is a straightforwards dive, see the introduction for details).

http://www.fourmilab.ch/gravitation/orbits/ and textbooks like MTW go into the math of how to calculate photon orbits, but don't present any visual picture of what one would "see" falling into a black hole.

The first website has a quiz section. Look at question #2

Click on the blue question mark to be directed to the answer:

For a quick "sanity check", let's consider the case where someone is falling straight in to a black hole, and is at the photon sphere at 1.5 x the Schwarzschild radius. For a stationary observer at this location, any photons emitted "in front" will fall into the black hole. To figure out what we see, we use the idea of ray tracing.

http://www.siggraph.org/education/materials/HyperGraph/raytrace/rtrace1.htm

We reverse time and ask "where would any visible photons come from"? We want a photon that originates at a distant star, and impacts our location. To do this, we reverse time and trace the outgoing path of a time-reversed photon, and see if it intersects any stars.

The black hole is black, so photons can't start from it. They must come from some object outside the black hole. We will assume that the light we see comes from some distant star, thus we need a reversed-time photon orbit that escapes to infinity.

We can see immediately that for the stationary observer, any such "reversed time" photons must come from behind the observer, not in front (because any photons emitted to the front fall in, any photons that come from the front must have come from the black hole, and the black hole is black).

A falling observer will see things differently due to relatavistic abberation due to his infalling velocity. This will make some of the photons which appeared to fall from "in back" of the stationary observer to be aberrated towards the front. So the black hole will not fill half the sky at the photon sphere for an infalling observer as one might expect. It will still fill a substantial portion of the sky, which will appear black. This seems to tie in reasonably well with the graphics on the website I mentioned earlier.

3. Dec 27, 2005

### wangyi

Thank you very much for your explanation and so many useful referances.

4. Dec 28, 2005

### Careful

**Hi, i am confused by the following question:
When an observer is going towards the horizon of a BH from outside, he finds the light from far away so blue shifted that the far future of the far away world presents in front of him. Does that mean when he is crossing the horizon, he has seen everything in the infinite future?
If it's true, there are questions:
1. Does this break the causal principle? As the observer has got information of the whole universe, including information outside his particle horizon.
2. When he has droped into the BH, what can he see? As he has seen everything before he drops into the BH, and what he sees after he goes cross the horizon seems to be at time "after" infinity.
Thank you! **

Not at all ! You must understand that the blueshift of light occurs with respect to the clock of the stationary observer which never falls into the black hole. The geometry at the event horizon is as good as Minkowski in Rindler coordinates and solutions to the Klein Gordon equation approximately behave as plane waves (in those coordinates). However, it is the stationary congruence of observers which gives rise to a singular coordinate transformation, whence the infinite blueshift as you approach the horizon. Actually, the worldlines of the stationary observers are infinitely squeezed together due to very large boosts (in the Rindler coordinates) as you approach the horizon (thus the measure sticks are infinetly expanded) which explains why those observers experience an extreme blueshift.

On the other hand, inertial observers in the Rindler coordinate system will not feel anything special when they cross the horizon and there is certainly no violation of causality.

Cheers,

Careful