What happens to stars in front of a falling observer entering a black hole?

[Passionflower]

It is often said that passing the event horizon for a large black hole is basically a non event as the size of the tidal acceleration at the event horizon depends on the mass of the black hole.

But let's consider something else; what happens to the stars in front of a free falling observer falling radially at escape velocity into a black hole. Can we devise a formula that expresses the red or blue shift as seen by the observer?

We have the redshift formula for stars behind us, which is:
\sqrt { \left| \left( 1-\sqrt {{\frac {r_{{s}}}{r}}} \right) \left( <br /> 1+\sqrt {{\frac {r_{{s}}}{r}}} \right) ^{-1} \right| }{\frac {1}{<br /> \sqrt { \left| 1-{\frac {r_{{s}}}{r}} \right| }}}
Which graphically looks like:
http://img442.imageshack.us/img442/4100/redshift.png
But what do we measure about the stars ahead of us?

 

[edgepflow]

Yes, the result is:

\lambda_{shift} = \lambda_{0} \sqrt{1 - R_{s}/R_{hover}{}}

Reference: "Black Holes A Traveler's Guide", P.37, Pickover.

 

[pervect]

I don't have "Traveller's guide", but the quoted expression looks like it's for a hovering observer (because of the R_hover).

The black hole itself blocks most of the light from the "other side".

For the falling case, see for instance Andrew Hamilton's webpage, http://casa.colorado.edu/~ajsh/approach.html#lensing.

Picking out the most relevant part of the webpage:

n the illustrated case, the lensing mass is a black hole. Any light rays which come within 1.5 Schwarzschild radii of the black hole fall into the black hole. Here there is a dark region, bounded by the red lines, within which images of background objects cannot appear.

For what you see after you pass through, look a bit later on the webpage, http://casa.colorado.edu/~ajsh/singularity.html, "The Schwarzschild bubble".

I've ommited some things that appear not to be directly relevant to the origianl question that are still interesting, including some interesting discussion about how and when one sees people who have previously fallen through the horizon.