# Collapse to a ring singularity

• stevebd1
In summary, the conversation discusses the concept of a rapidly rotating star collapsing into a ring singularity at the speed of light. There are two proposed theories for the reduced circumference of the ring singularity, one based on the conservation of angular momentum and the other taking into account the effects of special relativity. The latter theory suggests that the coordinate radius of the ring singularity can be expressed as a function of the angular momentum and the tangential velocity, and provides a better approximation for the reduced circumference of the ring singularity. However, the exact nature of what happens inside a black hole is still not fully understood.
stevebd1
Gold Member
One thing I’ve always found a bit of a curiosity is how a rapidly rotating star might collapse to a ring singularity relative to the speed of light and what the final parameters of the ring singularity might be (i.e. reduced circumference considering r=0 at the ring edge). Due to the conservation of angular momentum, I have seen suggestions that the reduced circumference would be based on $J=vmr$ (see ref. 1 below). Based on $c$ being the maximum velocity, this is rearranged to give the quantity $a$ where $a=J/mc$ but this puts the ring singularity between the outer and inner event horizon, implying that the RS would hold a ‘stable’ orbit in space-like spacetime which would be like us hovering ‘constantly’ at 1.00 pm. This didn’t seem correct but the only other option is that the tangential velocity of the collapsing star would exceed $c$ locally (the proper tangential velocity would exceed c due to frame-dragging) in order for it to collapse within the Cauchy horizon, again, this had it’s own problems (i.e. local superluminal velocity).

I had a look on the web and found the following question/answer- http://answers.yahoo.com/question/i...HDCpA4jzKIX;_ylv=3?qid=20081218053035AAT9JKE" which I thought gave a fairly decent answer. Basically, as the star collapses, the Lorentz parameter has an effect on the linear momentum part of the angular momentum equation-

Newtonian equations for angular momentum-

$$J=rp$$

Where $J$ is angular momentum, $r$ is radius and $p$ is momentum where

$$p=mv$$

Where $m$ is mass and $v$ is velocity (in the case of a rotating object, tangential velocity)

Combining both equations produces-

$$J=vmr$$

In special relativity, linear momentum becomes

$$p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}$$

Which means the coordinate radius of a ring singularity might be expressed as

$$r=\frac{J\sqrt{1-\frac{v^2}{c^2}}}{mv}$$

Based on 3 sol mass black hole with a spin parameter of a/M=0.95 and a potential tangential velocity of 0.99c for the ring singularity, provides an approximation for the reduced circumference of the RS of r~600 mm which puts it well within the Cauchy horizon (r=0 considered to be at the outer edge of the ring singularity in some models of a rotating black hole and any space inside the ring would be considered negative) while a=J/mc still plays a part in the Kerr metric (having parallels with the gravitational radius). While it's apparent that what goes on inside a black hole is not fully understood, this seems a better proposal than simply r=J/mv.

I'd be interested to hear other peoples opinions regarding this.(1)The Kerr Black Hole by Max Camenzind & A. Müller
http://www.lsw.uni-heidelberg.de/users/mcamenzi/GR_07.pdf
p 206 fig. 7.4 p 209 fig. 7.8

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Want to discuss with you but: every time you want to write: stellar black hole and state neutron star instead i'll get serious otherwise I get furious! If you want explanation why you can ask that, if you don't pass this boarder also ok. I know much about rotating gravitational objects and the model of a doughnout is for me just looking to past correspondence with professors of open mind.

Thank you for sharing your thoughts on the concept of a collapsing star forming a ring singularity. I agree that it is a fascinating and complex topic that is still not fully understood. I also found the proposed explanation in the Yahoo Answers link to be quite informative and thought-provoking.

The idea of the reduced circumference of the ring singularity being based on the Lorentz parameter and the linear momentum part of the angular momentum equation certainly seems like a more accurate approach than simply using J=vmr. It takes into account the effects of special relativity and provides a better understanding of the dynamics involved in the formation of a ring singularity.

I also appreciate your mention of the Kerr metric and its parallels with the gravitational radius. It is interesting to consider how these different factors play a role in the formation and behavior of a black hole.

Overall, I believe that the concept of a collapsing star forming a ring singularity is a complex and intriguing topic that requires further exploration and discussion. I look forward to hearing other perspectives and opinions on this matter. Thank you for sharing your insights.

## 1. What is a "collapse to a ring singularity"?

A "collapse to a ring singularity" is a theoretical concept in physics that describes the collapse of a massive object, such as a star, into a singularity in the shape of a ring. This is a potential outcome of the process of gravitational collapse, where the object's own gravity becomes so strong that it causes it to collapse in on itself.

## 2. How does a "collapse to a ring singularity" occur?

In order for a "collapse to a ring singularity" to occur, a massive object must have a very high density and rotation rate. As it collapses, the conservation of angular momentum causes the object to flatten into a disc-like shape, and the strong gravitational forces cause the inner part of the disc to continue collapsing until it forms a ring-shaped singularity.

## 3. What are the implications of a "collapse to a ring singularity"?

If a "collapse to a ring singularity" were to occur, it would result in a massive release of energy in the form of gravitational waves. This could have significant effects on the surrounding space-time, potentially causing ripples and distortions that could be observed by gravitational wave detectors.

## 4. Can a "collapse to a ring singularity" be observed?

Currently, there is no evidence to suggest that a "collapse to a ring singularity" has occurred in our observable universe. However, there are ongoing efforts to detect gravitational waves that could potentially be produced by such an event, which could provide indirect evidence for its occurrence.

## 5. Is a "collapse to a ring singularity" a possibility for our own Sun?

No, a "collapse to a ring singularity" is not a likely outcome for our Sun. While it will eventually exhaust its nuclear fuel and collapse into a white dwarf, it does not have the necessary characteristics, such as high enough density and rotation rate, for a "collapse to a ring singularity" to occur.

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