Understanding the Kerr Metric: Solving for Delta and Lambda functions

In summary, multiple references agree on the form of the Kerr metric, with the only difference being the symbol used for the function \Delta/\Lambda^2. There is no clear consensus on which symbol is correct, but all references provide the same equation solution for the Kerr metric.
  • #1
Orion1
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According to Wikipedia, the equation for the Kerr metric is:
[tex]c^{2} d\tau^{2} = \left( 1 - \frac{r_{s} r}{\rho^{2}} \right) c^{2} dt^{2} - \frac{\rho^{2}}{\Lambda^{2}} dr^{2} - \rho^{2} d\theta^{2} - \left( r^{2} + \alpha^{2} + \frac{r_{s} r \alpha^{2}}{\rho^{2}} \sin^{2} \theta \right) \sin^{2} \theta \ d\phi^{2} + \frac{2r_{s} r\alpha \sin^{2} \theta }{\rho^{2}} \, c \, dt \, d\phi[/tex]

However, according to four other references listed in Reference and equations listed as attachment for brevity, the 'Delta/Lambda' function is not squared within the metric?

[tex]\frac{\rho^{2}}{\Lambda^{2}}[/tex] ?

Which equation reference is the correct equation solution for the Kerr metric?

Reference:
http://en.wikipedia.org/wiki/Kerr_metric#Mathematical_form"
http://relativity.livingreviews.org/open?pubNo=lrr-2004-9&page=articlesu25.html" [Broken]
http://www.astro.ku.dk/~milvang/RelViz/000_node12.html" [Broken]
http://arxiv.org/PS_cache/gr-qc/pdf/0201/0201080v4.pdf" [Broken]
http://www.authorstream.com/Presentation/Waldarrama-31254-Kerr-Metric-Rotating-Electrically-Neutral-Black-Holes-Assumptions-Derivation-Abridged-Wh-the-as-Entertainment-ppt-powerpoint/" [Broken]
 

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  • #2
I have checked the Wikipedia reference, the first two links that you give after Wikipedia, and two references that I happened to take home tonight, and all (including Wikipedia) agree on the form of the Kerr metric.

What most references call [itex]\Delta[/itex], Wikipedia calls [itex]\Lambda^2[/itex]. When these symbol are replaced by their defining expressions, everything works out the same.
 
  • #3
Orion, what do you do/what level are you at career wise. Every post you make is either a question I'm currently working on or have a question about. I feel like we're doing the same thing. Tell me about yourself, maybe we can collaborate.
 

1. What is the Kerr Metric?

The Kerr Metric is a mathematical model used in the field of general relativity to describe the spacetime around a rotating massive object, such as a black hole. It was first developed by physicist Roy Kerr in 1963.

2. How is the Kerr Metric solved for Delta and Lambda functions?

The Kerr Metric is solved by using a combination of mathematical techniques, including differential equations and tensor calculus. The Delta and Lambda functions are calculated based on the mass and angular momentum of the rotating object, as well as the distance from the center of rotation.

3. What is the significance of solving for Delta and Lambda functions in the Kerr Metric?

The Delta and Lambda functions are important components of the Kerr Metric as they help describe the curvature of spacetime around a rotating object. They also play a key role in calculating various physical properties, such as the event horizon and ergosphere, of the rotating object.

4. What are the practical applications of understanding the Kerr Metric?

Understanding the Kerr Metric is essential for accurately modeling and predicting the behavior of rotating objects in space, such as black holes and neutron stars. It also has implications for understanding the structure of the universe and the nature of gravity.

5. Is the Kerr Metric the only model used to describe rotating objects in space?

No, there are other mathematical models used to describe rotating objects, such as the Schwarzschild Metric and the Reissner-Nordström Metric. The Kerr Metric is specifically designed to describe the spacetime around rotating objects and is the most commonly used model for this purpose.

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