# Kerr metric

1. Aug 8, 2008

### Orion1

According to Wikipedia, the equation for the Kerr metric is:
$$c^{2} d\tau^{2} = \left( 1 - \frac{r_{s} r}{\rho^{2}} \right) c^{2} dt^{2} - \frac{\rho^{2}}{\Lambda^{2}} dr^{2} - \rho^{2} d\theta^{2} - \left( r^{2} + \alpha^{2} + \frac{r_{s} r \alpha^{2}}{\rho^{2}} \sin^{2} \theta \right) \sin^{2} \theta \ d\phi^{2} + \frac{2r_{s} r\alpha \sin^{2} \theta }{\rho^{2}} \, c \, dt \, d\phi$$

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?

$$\frac{\rho^{2}}{\Lambda^{2}}$$ ???

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]

#### Attached Files:

• ###### DELTA001b.JPG
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Last edited by a moderator: May 3, 2017
2. Aug 8, 2008

### George Jones

Staff Emeritus
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 $\Delta$, Wikipedia calls $\Lambda^2$. When these symbol are replaced by their defining expressions, everything works out the same.

3. Aug 8, 2008

### K.J.Healey

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.