Why doesn't a real Infinite Redshift Limit occur at R+ for Kerr BHs?

[JTorn]

Homework Statement

The exercise says the following:

" Considering a body radially infalling towards a Kerr black hole, show that ˙t becomes infinite at the horizon r = r+ but not at the static limit r = R+. Although the r = R+ surface is usually called “infinite redshift surface” (because gtt = 0 there), argue that this is not where the actual infinite redshift takes place (as seen from infinity). What prevents a source of light from being infinitely redshifted at R"

Relevant Equations

We got the formulae for EH raidus (r+) and the radius for Ergosphere (R+).

As I have studied before, I found that Infinite Red Shift occurs where g_tt = 0 but this exercise says that on Kerr's Black Hole it doesn't really work like that.

Right now I'm blocked because I didn't find anything on the internet about it so I don't know how to show this phenomenon. Any help would be great.

 

[JTorn]

Guess that none knows the answer.