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

• JTorn
In summary, the lack of a real Infinite Redshift Limit at R+ for Kerr BHs is caused by the rotation of the black hole, which creates a frame-dragging effect that reduces the gravitational pull at the event horizon. This effect always prevents the redshift from becoming infinite. The rotation of a black hole also affects the redshift at the event horizon by decreasing the gravitational pull and can never cause the redshift to become infinite. Other factors such as mass and charge of the black hole can also affect the redshift. Additionally, the rotation of a black hole affects the shape and size of the event horizon, which is closer to the black hole at the poles and farther away at the equator due to the oblate shape of
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 gtt = 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.

Guess that none knows the answer.

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

The Infinite Redshift Limit, also known as the gravitational redshift, is a phenomenon where light appears to have an infinite wavelength and thus zero frequency as it approaches the event horizon of a black hole. However, this limit does not occur at the R+ horizon for Kerr black holes due to the effects of frame dragging and gravitational lensing.

## 2. What is frame dragging?

Frame dragging is a relativistic effect in which the rotation of a massive object, such as a black hole, causes the surrounding spacetime to be dragged along with it. This results in a twisting of the spacetime fabric, which can affect the motion of particles and light near the black hole.

## 3. How does frame dragging affect the redshift limit?

Frame dragging can alter the path of light near a black hole, causing it to curve and potentially avoid the event horizon. This means that the light does not experience the full effects of the black hole's gravitational pull, resulting in a smaller redshift than what would occur at the event horizon.

## 4. What is gravitational lensing?

Gravitational lensing is another effect of general relativity in which the path of light is bent by the presence of a massive object, such as a black hole. This can result in the distortion or magnification of objects behind the black hole as seen from our perspective.

## 5. How does gravitational lensing affect the redshift limit?

Similar to frame dragging, gravitational lensing can also alter the path of light near a black hole. This can result in a shift in the observed wavelength of light, which can affect the redshift limit. In the case of Kerr black holes, the combined effects of frame dragging and gravitational lensing can prevent the Infinite Redshift Limit from occurring at the R+ horizon.

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